The Collaborative International Dictionary of English v.0.48:

Rani \Ra"ni\ (r[aum]"n[=e]), n. [Hind. r[=a]n[imac], Skr.
   r[=a]jn[imac]. See Rajah.]
   A queen or princess; the wife of a rajah. [Written also
   ranee.] [India]
   [1913 Webster]

WordNet (r) 3.0 (2006):

rani
    n 1: (the feminine of raja) a Hindu princess or the wife of a
         raja [syn: rani, ranee]

Moby Thesaurus II by Grady Ward, 1.0:

21 Moby Thesaurus words for "rani":
   Kaiserin, begum, crown princess, czarina, empress, grand duchess,
   infanta, kumari, kunwari, maharani, malikzadi, princess, princesse,
   queen, queen consort, queen regent, queen regnant, raj-kumari,
   shahzadi, sovereign princess, sovereign queen