Nope, we get sent papers to review and are expected to read and send a report of them without compensation, as part of our scientific responsibility.

There have been attempts to speed up publication by offering cash bonuses ($20-$50) if you return your review in a timely fashion (as you can imagine some reviews take a really long time since there is no hard incentive to do it) but these amounts still pale in comparison to the several hours or more that you are asking of an expert's time.

I have never heard of peer reviewers being paid in my discipline (materials science). Even the editor is usually a volunteer, though sometimes they are paid a small honorarium...