The answer is, "Yes, BUT..."
Ro2--A .223 can be used to hunt deer (where legal.) It will kill deer. However (there is always that darn "however!") you will have to be man enough to pass up "iffy" shots that would be easy kills for a slightly larger cartridge.
Should the deer be standing broadside to you, unhindered by brush, and > than, say, 75 yd, you could kill it humanely with a .223--always given that you are a good enough shot, of course, but since that proviso applies no matter what the caliber, it is not part of this equasion.
Now, if the deer is in a more usual situation, sneaking through the brush, running, distant, hiding among trees, etc, etc--all the usual Murphy factors--then you want more insurance than the .223 provides.
You will get posts from people who say they routinely kill truckloads of deer with .223's. I wonder how many deer escape from these people, wounded, to die in agony later and be wasted. All I can say about that is, I wouldn't.
The .243 Win is usually considered to be the MINIMUM humane deer hunting cartridge, and even with that, there are "iffy" shots to pass on.