I'm going to ask my roommate to lock the door
That is good to have the house secured.
I feel uncomfortable when it isn't locked.
Asking your roommate to lock the door is a completely reasonable request. It makes sense that you'd feel safer with the door locked. I'm sure your roommate will lock the door from now on because you've asked them to.
I'm going to ask him again and if he thinks I'm annoying, I might move out then.
It's good you're trying to communicate with them that you want the door locked. Although, I think it's a bit rash to want to move out if they don't lock it. Try to explain that would make you feel a lot more comfortable.