There are some special cases in tag questions. For instance,
(((I am right, aren't I? aren't I (not amn't I)
You have to go, don't you? you (do) have to go...
I have been answering, haven't I? use first auxiliary
Nothing came in the post, did it? treat statements with nothing, nobody etc like negative statements
Let's go, shall we? let's = let us
He'd better do it, hadn't he? he had better (no auxiliary))))

Now answer to your question is:
I have to complete my essay, don't I? The tag ending is "don't I".