It is a proper question. We just change the intonation.
Я кіт - I'm a cat
Я кіт? - Am I cat?
We also have this question word чи that can clearly mark a sentence as a question, so you can ask:
Чи я кіт? Am I cat?
But it makes sentence sound more formal, and while some people do use it in their daily speech, it sounds quite bookish to me.