"It's I" is correct. "I" is acting as a subject complement and takes the subjective case.
That said: everybody I know says "It's me." There is even an old and not very funny joke:
St. Peter (at pearly gates): Who is it?
Voice: It is I!
St. Peter: Go to hell, we already have all the English teachers we need!
[disclaimer: I am a native speaker and hold an English undergraduate degree, but am not a teacher]