私は料理が上手です is the correct expression. You're stating "I'm good at cooking" in a direct sense.
Compare it to this sentence: 私は料理を作るのが上手です。Literally translated: "I'm good at making food". As you can see, we used を after 料理 because of the verb 作る. But since (料理) is something which is naturally "made or cooked", we don't have to mention the verb (作る). Therefore it's more preferable to use the sentence: 私は料理が上手です。