Is There A Word For A Person (other Than Magician) Who Uses Magic?

Yes, you can use the words conjurer, sleight-of-hand technician, illusionist or any other word that relates to the art of illusion.

When you say "Uses Magic" it gives the impression that you mean the real Magic, the great work and not the amusement art. Any human being who is aware of the forces within and in the nature can do Magic. When you blow a candle on your birthday cake making a wish when you were a kid, that was the easiest spell-work. Magic is a way of empowering the intentions with the forces within and the forces of nature. The intentions should be always good, for that what you do, shall come back to you, three times.
Blessed Be!

A witch, warlock, wiccan.... These all have some sort of magic in their worship.