The Collaborative International Dictionary of English v.0.48:

Affiant \Af*fi"ant\, n. [From p. pr. of OF. afier, LL. affidare.
   See Affidavit.] (Law)
   One who makes an affidavit. [U. S.] --Burrill.
   [1913 Webster]

   Syn: Deponent. See Deponent.
        [1913 Webster]

WordNet (r) 3.0 (2006):

affiant
    n 1: a person who makes an affidavit