From Guns.com:

As the AR design has reached maturity, large-frame and small-frame rifles have become prevalent. This means that gun owners and hunters have many more options to choose from. Small frame AR’s run traditional cartridges like the .223/5.56, which have always been a good choice for hunting small game and varmints. 

If bigger game is on your list, then a large-frame AR chambered in something like 6.5 CM or .308 Winchester would be an excellent option. There are even a few companies out there making XL-framed AR-style rifles that are chambered in magnum cartridges, making nearly any North American animal potential prey. All this while maintaining the same modularity and manual of arms common to the AR-style rifle. This extremely adaptive nature of the AR continues to open doors for its use in hunting purposes.