If you have a .223 Remington AR-15, you need to check your state laws. They vary from state to state, and many states won't allow you to hunt large game such as deer with anything in the .22-caliber range-- even centerfire rounds such as the .223. You can generally hunt varmints, though, such as coyotes, but you'll need to be a very good shot to humanely put them down with a .223.
If your AR-15 is chambered for .308 or some other large center-fire round (of the literally dozens of chamberings for AR-platform rifles, including the same .50 BMG that is in the ever-so-famous Barrett), you'd be able to hunt deer just fine [Edit: You shouldn't hunt with a .50 BMG. Ever. Unless you're hunting light armor or a Graboid!]. There are also .22LR ARs which would only be suitable for squirrel or rabbit, generally.