Zoro is the first mate. If not for any other reason than him technically being the first nakama that Luffy recruited.
Thank you for your input DiableShoot. It will now be disregarded because that is not what "first mate", the position on a ship, denotes.
No where in any dictionary (that I can find) does the definition of "first mate" read "first to join the captain on the ship".
You are not the first one to suggest this but the order of which the strawhats joined Luffy is as irrelevant as to whom can pee the furthest over the railing when deciding the positions in the crew. Just look at the musician. Luffy wanted one since forever, But the position wasn't filled untill Brook came along.