"It is I who is waiting for you."
First of all, the correct pronoun here is "I," not "me." That's because "I" is NOT the object of the verb "is." You are expressing equivalence, not the target of an action. This is one of these awkward cases. All careful speakers with sensitivity to grammar agree that "It is I" is correct and that "It is me" is incorrect. However, because the pronoun follows the verb, it "feels like" an object, and thus people follow the habit pattern and use the object pronoun. This is so very common that you can't really say it's wrong.
Why do I say "is waiting?" I'm a native U.S. speaker but not a grammarian. My intuition is this. Even though "who" follows "I", is NOT referring to "I." It is referring back to "It." Thus, the structure of the sentence is not
"I am waiting for you,"
it is
"It is waiting for you."