This is what the OED has under the etymology of "algorism" slightly modified for easier posting:
Actually the linked site has a very good entry on both "algorism" and "algorithm".
So Pipes, Michelle Malkin, Geller et al should pay attention: The words alcohol, algebra and algorism are all really Arabic.
Algorisme being popularly reduced in OFr. to augorime, English also shows two forms, the popular augrime, ending in agrim, agrum, and the learned algorism which passed through many pseudo-etymological perversions, including a recent algorithm in which it is learnedly confused with Gr. number.'
Nevertheless, to understand the game aright, they feared neither the cormorant nor mallard of Savoy, which put the good people of my country in great hope that their children some time should become very skilful in algorism.