itch.io

And take the "fun" away from discovering them yourself? 

But to elaborate on your original question, you cannot do this inside your game, since the player is not logged in as an itch user. What you can do, is what magic said, you can put a link in your game, so the browser of the player opens and if the player is logged in, now rating can commence.

On your game page and in the game you can of course do what all the youtubers do. Begask for comments, likes and subscribe.

Now, some unrelated things I found out.

2fa protection does not do anything against cookie theft attacks.

There is a ton of malware on itch, new is uploaded daily, including hacked accounts, so do not trust anyone, just because they are hosted on itch, not even if the file is two years old - it takes a lot more to earn the trust needed to execute files from a stranger, an amateur developer at that, most of the time. 

There is an itch app. 

Reviews are not public to the game, but might be public to the feed. And a rating and a review is one and the same. One could say, a rating is a review without text.

There is a community forum on itch.

There are more people hating horror and commenting about it, then there are people liking horror and commenting about it, even though the most popular by far genre is horror.

You can searchfilter for tags and the box to filter tags is a write in box, not a pure select box.

You cannot search tags. Although, you can, but only those that are in the predefined list of that box.

The search button searches titles. Like, literally. It is not a genral purpose search box. If you find something without a title match, it was a manually created alias or there were not enough results and the box did do a tiny bit description search.

Pay what you want is a thing.

The css designers of itch have huge displays and a fine eyesight. (Try zooming in and see elements disappearing).

Games can be jammed.