The Collaborative International Dictionary of English v.0.48:

anaesthetize \a*n[ae]s"the*tize\, anesthetize \a*nes"the*tize\,
   ([a^]n*[e^]s"th[-e]*t[imac]z), v. t. (Med.)
   To produce anesthesia by an an[ae]sthetic. --Encyc. Brit.
   [1913 Webster + AS]

The Collaborative International Dictionary of English v.0.48:

anesthetize \anesthetize\ v. t.
   To cause to become unconscious by administration of an
   anaesthetic agent. [Also spelled anaesthetize.]

   Syn: put to sleep, put under, put out.
        [WordNet 1.5 +PJC]

WordNet (r) 3.0 (2006):

anaesthetize
    v 1: administer an anesthetic drug to; "The patient must be
         anesthetized before the operation"; "anesthetize the gum
         before extracting the teeth" [syn: anesthetize,
         anaesthetize, anesthetise, anaesthetise, put under,
         put out] [ant: bring around, bring back, bring
         round, bring to]