It should be "It's you who is wrong". The word "who" refers to the subject "you", but inherits only the number (singular or plural) of the subject. Then "is" depends on "who". In this sense you can consider the phrase "who is wrong" as a (complex?) clause.

For instance, you wouldn't say "It's I who am wrong."

But curiously enough, with this construction you can actually distinguish between a singular "you" and a plural "you". How nifty! :)