Characterizing antigen-specific B cells is a critical component of vaccine and infectious disease studies in rhesus macaques (RMs). However, it is challenging to capture immunoglobulin variable (IgV) genes from individual RM B cells using 5’ multiplex (MTPX) primers in nested PCR reactions. In particular, the diversity within RM IgV gene leader sequences necessitates the use of large 5’ MTPX primer sets to amplify IgV genes, decreasing PCR efficiency. To address this problem, we developed a switching mechanism at the 5’ ends of the RNA transcript (SMART)-based method for amplifying IgV genes from single RM B cells, providing unbiased capture of Ig heavy and light chain pairs for cloning antibodies. We demonstrate this technique by isolating simian immunodeficiency virus (SIV) envelope-specific antibodies from single-sorted RM memory B cells. This approach has several advantages over existing methods for PCR cloning antibodies from RMs. First, optimized PCR conditions and SMART 5’ and 3’ rapid amplification of cDNA ends (RACE) reactions generate full-length cDNAs from individual B cells. Second, it appends synthetic primer binding sites to the 5’ and 3’ ends of cDNA during synthesis, allowing for PCR amplification of low-abundance antibody templates. Third, universal 5’ primers are employed to amplify the IgV genes from cDNA, simplifying the primer mixes in the nested PCR reactions and improving the recovery of matched heavy and light chain pairs. We anticipate this method will enhance the isolation of antibodies from individual RM B cells, supporting the genetic and functional characterization of antigen-specific B cells.