Is Tuesday named for a one-handed god?
c.1400, "to invoke spirits," from Old French exorciser (14c.), from Late Latin exorcizare, from Greek exorkizein "banish an evil spirit; bind by oath" (see exorcism).
Sense of "calling up evil spirits to drive them out" became dominant 16c. A rare case where -ise trumps -ize on both sides of the Atlantic, perhaps by influence of exercise. Related: Exorcised; exorcising.