Transcriptional mutagenesis (TM) due to misincorporation during RNA transcription can result in mutant RNAs, or epimutations, that generate proteins with altered properties. TM has long been hypothesized to play a role in aging, cancer, and viral and bacterial evolution. However, inadequate methodologies have limited progress in elucidating a causal association. We present a high-throughput, highly accurate RNA sequencing method to measure epimutations with single-molecule sensitivity. Accurate RNA consensus sequencing (ARC-seq) uniquely combines RNA barcoding and generation of multiple cDNA copies per RNA molecule to eliminate errors introduced during cDNA synthesis, PCR, and sequencing. The stringency of ARC-seq can be scaled to accommodate the quality of input RNAs. We apply ARC-seq to directly assess transcriptome-wide epimutations resulting from RNA polymerase mutants and oxidative stress.