"I" is the subjective case, and in your example, the "I" is a subject complement - "words following linking verbs that complete the meaning of the subject" - if it sounds odd or too stilted you can rewrite around it.
Mary admitted that the thief was she. Mary admitted that she was the thief.
"Me" is the objective case when it "functions as a direct object, and indirect object, or the object of a preposition."
Jon gave me a surprise party.
(quotes from "A Writer's Reference" by Diana Hacker)
But, going back to what Eric was saying about common usage, you need to look at the character who is saying it, or the context in which it is used. If you're writing a formal letter to someone, or if your character is a throwback from the 19th century or an English teacher, you would use the grammatically correct.
But if your character is a contemporary teenager or really pretty much anyone speaking informally one with another you'd use what sounds less stuffy--It's me. IE, if a twenty-something person snuck up behind someone else and whispered "It is I," into the ear of another person I would automatically make the assumption, if I didn't know better, that the story setting was Victorian England or that the character was a highly educated dweeb.
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