The Collaborative International Dictionary of English v.0.48:

Believer \Be*liev"er\, n.
   1. One who believes; one who is persuaded of the truth or
      reality of some doctrine, person, or thing.
      [1913 Webster]

   2. (Theol.) One who gives credit to the truth of the
      Scriptures, as a revelation from God; a Christian; -- in a
      more restricted sense, one who receives Christ as his
      Savior, and accepts the way of salvation unfolded in the
      gospel.
      [1913 Webster]

            Thou didst open the Kingdom of Heaven to all
            believers.                            --Book of Com.
                                                  Prayer.
      [1913 Webster]

   3. (Eccl. Hist.) One who was admitted to all the rights of
      divine worship and instructed in all the mysteries of the
      Christian religion, in distinction from a catechumen, or
      one yet under instruction.
      [1913 Webster]

WordNet (r) 3.0 (2006):

believer
    n 1: a supporter who accepts something as true [syn: believer,
         truster]
    2: a person who has religious faith [syn: believer,
       worshiper, worshipper]

Moby Thesaurus II by Grady Ward, 1.0:

35 Moby Thesaurus words for "believer":
   Christian, God-fearing man, accepter, catechumen, churchgoer,
   churchite, churchman, communicant, convert, cultist,
   daily communicant, devotee, devotionalist, disciple, fanatic,
   fideist, follower, good Christian, ist, neophyte, pietist,
   proselyte, receiver, religioner, religionist, religious believer,
   saint, the assured, the believing, the faithful, theist,
   true believer, truster, votary, zealot