Can it be done? Sure, would I advise it? Probably not. Just about any centerfire on the market will kill a deer if you use the proper bullet and put it in the vitals. Punctured lungs equal dead deer, every time. There might be some tracking to be done though. Don't think you are going to shoot one in the shoulder and drop it where it stands with a .223 though.

I would say a .223 would be a capable round in the hands of an experienced hunter, and it most cases (not all mind you) if you have to ask if it is ok for deer your probably not in that group. However if that is all you had to use until you get something a bit better I wouldn't tell you to stay out of the woods. Just know what your rifle is capable of and pick your shots wisely. Much like bowhunting, except at longer ranges.

Paul