The Collaborative International Dictionary of English v.0.48:

Mesmerist \Mes"mer*ist\, n.
   One who practices, or believes in, mesmerism.
   [1913 Webster]

WordNet (r) 3.0 (2006):

mesmerist
    n 1: a person who induces hypnosis [syn: hypnotist,
         hypnotizer, hypnotiser, mesmerist, mesmerizer]