Chemical modifications to messenger RNA are increasingly recognized as a critical regulatory layer in the flow of genetic information, but quantitative tools to monitor RNA modifications in a whole-transcriptome and site-specific manner are lacking. Here we describe a versatile platform for directed evolution that rapidly selects for reverse transcriptases that install mutations at sites of a given type of RNA modification during reverse transcription, allowing for site-specific identification of the modification. To develop and validate the platform, we evolved the HIV-1 reverse transcriptase against N1-methyladenosine (m1A). Iterative rounds of selection yielded reverse transcriptases with both robust read-through and high mutation rates at m1A sites. The optimal evolved reverse transcriptase enabled detection of well-characterized m1A sites and revealed hundreds of m1A sites in human mRNA. This work develops and validates the reverse transcriptase evolution platform, and provides new tools, analysis methods and datasets to study m1A biology.