Also faith healer, attested by 1874; from faith + healer. Faith-curer is from 1883.
The power which a man's imagination has over his body to heal it or make it sick is a force which none of us is born without. The first man had it, the last one will possess it. If left to himself, a man is most likely to use only the mischievous half of the force--the half which invents imaginary ailments for him and cultivates them; and if he is one of those very wise people, he is quite likely to scoff at the beneficent half of the force and deny its existence. [Mark Twain, "Christian Science," 1907]