Getting a visitor's profile url with facebook's like button?

Ok so I have a wild idea in mind, but in order to make it work, I need a way to access a visitor's facebook profile url from one of the available fb social plugins (i.e.: the like button, share, etc..)

The question is how?

The like button uses an iframe that loads the fb user data but is inaccessible via js due to it being a different domain than my site. So I can't pull the user's profile url from there.

I just need the profile url of the visitor. Is there another kind of plugin fb offers that will let me have users login to facebook without leaving my site, and then letting me have access to their data somehow?

Am I just dumb and not seeing that this can be done with facebook's application api ? lol

It sounds like something that could be done with the Open Graph API. Check the docs for that.