Can some one help me with this?

What kind of help do you want?

I am renting a room out from someone one on the lease but someone keeps trying to break it in my I am getting a alarm system can I charge them??

I am not on the lease

Charge them? Not unless you are a officer of the law or court.

you can call the police.

if you are not on the lease, you are essentially a guest. I don't believe you have any right to privacy as a guest

Make sure you get a receipt when you pay your rent and if someone tries to break in call the police. You are not on the lease but you are a subletter with rights. If you catch a thief in the process with your camera and the police see it, you can ask them what to do as they will enforce the law. Also make sure you have one or two good locks on your door and don't leave money lying around. If you can get a thief put away, you are doing a good service for everyone.

MOVE

Most likely you can. That is your private space, and most laws protect it.

If someone is trying to break into your room, presumably it's someone you share the home with. Why would you want to share a house with someone who's trying to break into your room. If you're not on the lease you are within your rights to move out (and I'd be out of there in a New York minute). Are they trying to break in while you're in there? If so, how long do you think it will be before they don't bother to wait until you're behind a locked door?