You think I'm a sucker, don't you.

Literal

Me [object-を] sucker [is-だ] [quotative-と] thinking-[state-ている]-[explanation-んだろう].

鴨 (かも, written in hiragana here) is a colloquial term for 'sucker, easy mark, gullible target' — originally 鴨 ('duck'), from the image of a plump, easy target waiting to be caught. The structure Xを Yだと思う ('think of X as Y') frames the accusation. んだろう combines んだ (explanatory) + だろう (conjecture), forming a rhetorical/accusatory tone ('you're thinking that, aren't you').