I know guys that use .22 cf rifles for deer hunting and do fine. I personally prefer .243 or bigger myself, just for the what if scenario that happens from time to time. My goto gun is a .280, and I love it.
I have killed one with a .22-250, she went right down...but again, not my cal of choice. Heck, as posted...been an awful lot of deer killed with a regular .22, and the .223 is a huge step up from that. I even know a guy that shot one with a .17 rimfire (not recommended LOL). That deer went right down with a neckshot. Deer are very fragile with the right shot placement.
Beyond shot placement, I believe bullet performance is the key to success with ANY gun. Much more important than bullet size, at least in my experience. I'm glad to see that better "deer" bullets are being made in the .22 size range now.