TRAM domain proteins present in Archaea and Bacteria have a β-barrel shape with anti-parallel β-sheets that form a nucleic acid binding surface; a structure also present in cold shock proteins (Csps). Aside from protein structures, experimental data defining the function of TRAM domains is lacking. Here, we explore the possible functional properties of a single TRAM domain protein, Ctr3 (cold-responsive TRAM domain protein 3) from the Antarctic archaeon Methanococcoides burtonii that has increased abundance during low temperature growth. Ribonucleic acid (RNA) bound by Ctr3 in vitro was determined using RNA-seq. Ctr3-bound M. burtonii RNA with a preference for transfer (t)RNA and 5S ribosomal RNA, and a potential binding motif was identified. In tRNA, the motif represented the C loop; a region that is conserved in tRNA from all domains of life and appears to be solvent exposed, potentially providing access for Ctr3 to bind. Ctr3 and Csps are structurally similar and are both inferred to function in low temperature translation. The broad representation of single TRAM domain proteins within Archaea compared with their apparent absence in Bacteria, and scarcity of Csps in Archaea but prevalence in Bacteria, suggests they represent distinct evolutionary lineages of functionally equivalent RNA-binding proteins.