PC Games Hardware explains in an article how to turn on DirectX 11 graphics in World of Warcraft.

They ran a benchmark test, and as the table graphic proves, World of Warcraft’s performance (15% FPS) and rendering is faster (by 20-60%) under DirectX 11 than DirectX 9.

Blizzard Entertainment unofficially started DirectX 11 support in Cataclysm beta patch v12694 and live realms patch 4.0.1.