The combination of ligation-based RNA capture methods and high-throughput sequencing has facilitated the characterization of transcriptomes and the identification of novel noncoding RNAs. However, current ligation-based RNA capture methods require RNA substrates with terminal 3’-hydroxyl groups, limiting their utility for identifying RNAs with modified termini like 2’,3’-cyclic phosphates. Cyclic phosphate-terminated RNAs are generated by endonucleolytic cleavages and self-cleaving ribozymes and are found as stable modifications on cellular RNAs such as the U6 spliceosomal RNA. We developed a method that uses the Arabidopsis thaliana tRNA ligase to add an adaptor oligonucleotide to RNAs that terminate in 2’,3’-cyclic phosphates. The adaptor allows specific priming by reverse transcriptase, which is followed by additional steps for PCR amplification and high-throughput DNA sequencing. Applying the method to total human RNA, we found 2836 sequencing reads corresponding to the 3’ terminus of U6 snRNA, validating the method. In addition to a large background of reads that map throughout abundantly transcribed RNAs, we also found 42,324 reads of specific fragments from several tRNA isoacceptor families, suggesting that this method may identify processing events previously undetected by other RNA cloning techniques.