There is no contracted form for "am I not" hence, "aren't I" is used instead. However, you can use "I'm late, am I not?" and it will still be correct. This is simply the complete way of phrasing it. It is the same for other pronouns: He is late, isn't he. → He is late, is he not? You are late, aren't you. → You are late, are you not? Only in using the contracted form for "am I not" will "aren't I" be used instead. Note that the correct way of phrasing it is "am I not" and not "am not i". ☺ Hope this helped.

Positive statements are followed by negative tag questions with 'not' usually contracted to 'n't' but with the first person singular 'I' the contraction 'I amn't' isn't used in England and America. We don't say 'I amn't Italian' we say 'I'm not Italian'. So you can't say 'I am late, amn't I? Contracted negative tags in the first person singular are therefore formed with aren't, even though grammatically this is not considered correct. I am late, aren't I? Some people may use am I not? But it's considered rather formal.

It is called an EXCEPTION. Here we always say "aren't I', never,"am not I". If you want to be bookish you could say "am I not?". But that is rare.