Absolutely

Here's the bare minimum you need to successfully join the roleplaying hobby:

• At least one other willing person
• Mutual communication

That's it, full stop.

The complexity and bar to entry into RPGs don't have to be high — as evidence, I give you any five year old I've ever met. Seriously, the way children develop social skills is through social play. If you can communicate well enough with someone to hypothesize a world and people in it, you can role play with them. I know this because I spent about two years playing D&D with some deaf friends via an interpreter.

Adults tend to be a bit more demanding in the fields of "fairness" and "verisimilitude". When they play roleplaying games, they add rules. At a guess, you've heard of D&D. To give you one end of the spectrum, some of the older versions feature about 600-800 pages of core rules and thousands of pages of optional material. It also requires a set of polyhedral dice (or an online roller). Optional gear includes a battle mat and some mini figures. Painted ones are nice, but I've used everything down to pieces of candy.

On the other side of the spectrum, you can find a variety of games that break any given assumption. For example, Roll For Shoes has seven rules, which fit on an index card. It requires only "normal" six-sided die, like you'd find in Monopoly or other traditional board games. Other systems throw out ideas like needing dice (the Amber Diceless RPG), or having a GM at all.

So, the only remaining question given your communication constraints is where you can find an online group to play a voice chat with. One option to check out is this site's built-in chat.

Yes, this is definitely doable.

1. First, there are RPGs that aren't that complicated and/or don't require dice. Consider skipping GURPS and Burning Wheel in favor of simpler ones like Microscope, Risus, FATE, etc. (We don't do specific game recommendations here, just because it doesn't work well with the site format, but if you're able to use the chat room, folks can offer suggestions.)

2. Even if you play a "standard" game with more rules (DND is the most enduringly popular), most of the complexity in most games I can think of is around the character creation process. There's not a ton of looking at the rulebooks during play in most groups. The standard flow is: Gamemaster describes a scene or situation. Players describe their actions. GM describes the result of their actions. It's fundamentally a verbal activity. So while it may be extra work, if you can use a screen reader with a PDF of the rules to familiarize yourself in advance, it definitely shouldn't be insurmountable. (Since many games have mechanisms for improving your character, you'll want a group that's either led by someone friendly who can talk you through the process each time - pretty common with newbies anyway - and/or levels up in between sessions, so there's less time pressure around reading and writing.)

3. Character sheets could be tricky. I don't know if you'd be able to use a large-format or fillable PDF sheet, or not. A text file might work, but there's an argument for picking a less complex game that doesn't require keeping track of a dozen things on a character sheet. However, many games require you to keep track of something - hit points, fate points, whatever - so you may need to find a tactile way to do that (stacking cubes?) or else keep a separate text or calculator window open with just that number as you update it.

4. Games that are heavily dependent on a battle map are probably out, but this is optional at most, and difficult to pull off over the net without special tools, so especially since you're playing online it shouldn't be a big deal. Just something to be aware of.

5. Dice, fortunately, should be no problem. Any online rpg group should have a way to roll dice online; the one my group uses is rolz.org, but there are many more.

How to get started

That's a pretty big question. Fortunately, others have covered various aspects of getting started with RPGs on this very site; check out the new-players tag to browse, or try searching for your specific concerns. For starters, check out Finding online RPG players for a play-by-chat RPG Campaign?

My experience says it works fine.

I was in a gaming group a few years ago that had a player who was losing his sight; by the last time I played with him, he was effectively totally blind -- he used a screen reader, had PDF files of the rules books he needed, used a computer character generator or spreadsheet that worked with his screen reader. We were playing face to face, but it would work the same way via chat, except that another player can't help instantly if your computer develops a problem during the game or between games.

During the time I knew him, we also introduced his wife, who was partially sighted, to gaming (with GURPS, no less; 500+ pages of core rules and a deserved reputation for complexity, though it can be dialed back if the players and GM choose). Generally, being new to gaming will be a larger factor than visual limitations, and other players are virtually always happy to accommodate having to be told what to roll and when as needed while you internalize the game's mechanics.

If you were formerly sighted, you'll probably have no trouble visualizing the situations, though you'll have to play Theater of the Mind even if others are using miniatures (unless you have enough vision to check your miniature movements via video chat). Beyond that, I'd recommend reading the player portion of the core rules for your chosen game at least once (more, if you need to), so you understand the game mechanics before you start. That won't make you proficient, but it'll give you the grounding to become proficient more quickly. Depending on the chosen game, there may be free or paid applications to assist with character creation, but many/most GMs in my experience are happy to help outside play session time; this is usually considered a good idea even with experienced, fully able players, to ensure the characters fit the campaign.

It shouldn't be a problem at all.

I've played a lot through the Internet in the last few years with a variety of groups, mostly as a GM. My experience mostly comes from WFRP2, which is while not the most rule-heavy system, but still very much a traditional RPG. So to address your concerns.

Not being able to read the rules on the fly

Not a problem, it is the GMs job to know the rules, and I've met a lot of players who prefer playing instead of book-crunching. Also, if one plays in multiple, different systems the small details tend to be forgotten, as one cares about the rules that affect his/her character. So don't worry about it, GMs have to explain to rules to a lot of players. It is faster and easier to everybody if they do and the players don't spend a lot of time with reading the rulebook.

Getting new information through the narrator

It is the traditional way for everybody, and depending on the group this is the only way to get new info, especially if the GM is lazy and doesn't like to prepare handouts/maps. It is important that you talk with the GM before you start playing, you might not enjoy a campaign with intricate battle-maps and tactical combat as much as a more social/cinematic playstyle.

Dice

It is generally useful (and through the Internet it is fairly simple) to sit down with the GM before you start playing where she/he can explain the basic rules. Setting up a Skype/Hangouts/Teamspeak/whatever call is much easier than meeting up somewhere. I strongly advise you to do this when you find a GM. Once you know what dice to roll, online games use dice-rollers, and while I don't know how accessible they are to the visually impaired, rolling should be possible and I think you can trust the others to tell you the results.

How to get started

I sadly can't give any advice in this, unless you are Hungarian. You should check out other questions or answers.

Conclusion

So to conclude, being visually impaired won't be a problem online for a good amount of playstyles, but you should talk with the GM before you start rolling. It might be worth to check out different dice-rollers (roll20, rolz.org, etc) to find the easiest to use, but that is not an insurmountable problem. Find a nice GM and you are golden.

I have a little experience with this, having been part of a D&D 3.5 campaign with a visually impaired player, who was not formally sighted, for a couple of years. This was some time ago, but I believe they used a braille display and screen reader software to navigate character sheets and rules and the game was played face-to-face rather than online.

My experience is that an eagerness to learn/participate on the part of the VI player and a willingness to assist with descriptions and rules on the part of the others was sufficient. If you have a cooperative group then everything else will fall into place.

D&D 3.5 has rather strict combat mechanics which play out over a grid and this made thing a little bit awkward on occasion. It was necessary to carefully describe the relative locations of players, creatures and items as well as the shape and size of the spaces we were in which was a little foreign to most of the players as we were used to just using hand-drawn maps and placing miniatures, but we quickly adapted.

Whilst this generally worked out fine, we had a LOT of near misses and a few near hits from unexpectedly large Fireballs! This may have been more down to the player character's rather carefree, yet aggressive, use of magic rather than any mechanical issues however.

Long story short - yes you can, just be careful with your area of effect spells!

The overwhelming answer, is yes you can. However, and I'm surprised nobody else mentioned this, please choose your group carefully. As with any group of people, there are bound to be a few rotten apples. I'm sure you've encountered at least a few people who have treated you poorly for your lack of vision. As wrong as it is, there are definitely people in the hobby who would subject you to more of the same. Most people in the hobby are pretty nice, (though many are somewhat naive) so it shouldn't be too hard to find a good bunch. Just avoid getting stuck with a jerk if you can.

In particular, try to find a game host (the person organizing the event, regardless the system or their title) who is very patient and is good at teaching newbies. Someone who is confident and cares about the people at their table. If they are experienced with the system, all the better. Try to get to know the person in charge of the group a little bit before you commit to any sort of game. The last thing any new gamer needs is a stream of ignorance spilling out at them while they're trying to have fun learning a new game.

And of course, if it isn't fun, you are not obligated to keep playing. Bad play is worse than no play at all.

“I don't want to always be the person the GM has to explain things to.”

Other answers have given what I’d consider some good, general encouragement. But you’ve specifically stated that what you don’t want is to be the one person other folks need to “help out,” so this answer provides tips to keep that from happening.

Make sure the game you choose has rules in digital format

A given role-playing game may have all, some, or none of its rules available in digital format, accessible to your screen reader. The ones with all the rules available would be ideal, of course. There’s no need to overdo this, but you can become as familiar as you like with the rules before you begin.

Know your character well

This is good advice for anyone, but many folks never do it. Everyone should know the basic statistics your character will use most. A little extra time and you can put everything about a simple character to memory. If you do, you’ll be faster than others at your table, who have to check their character sheets.

Find a “Theater of the Mind” campaign

While some groups role-play with a physical or virtual map, others eschew this, and rely entirely on the descriptions of the game master to determine where things are and what can be done. Favor these theater-of-the-mind groups if you never want to worry about moving your token or mini to the needed place.

If you are going to use a game play app like roll20, learn its macro system, or find someone who knows it

A couple years ago, roll20 introduced character sheets, which were a great advance for many, since many of the rolls you needed to make were now “just a click away.” But this was in some ways a step backward for accessibility, because you have to be able to read the character sheet to use it effectively.

Macros, on the other hand, let you do the same thing with a few keystrokes.

Brailled Dice

A group that rolls its own dice should not be a blocker for you. There are braille dice that have been well-received, as well as large, high contrast dice for those with impaired visual acuity.

Play to your strengths

If you’re funny, likable, organized, attentive, creative, tactical, etc., you’ll be an asset to any gaming table you join. These are the important things for a role-playing game.

Best of luck, I think you’ve got a lot of fun ahead of you.