Current approaches to single-cell RNA sequencing (RNA-seq) provide only limited information about the dynamics of gene expression. Here we present RNA timestamps, a method for inferring the age of individual RNAs in RNA-seq data by exploiting RNA editing. To introduce timestamps, we tag RNA with a reporter motif consisting of multiple MS2 binding sites that recruit the adenosine deaminase ADAR2 fused to an MS2 capsid protein. ADAR2 binding to tagged RNA causes A-to-I edits to accumulate over time, allowing the age of the RNA to be inferred with hour-scale accuracy. By combining observations of multiple timestamped RNAs driven by the same promoter, we can determine when the promoter was active. We demonstrate that the system can infer the presence and timing of multiple past transcriptional events. Finally, we apply the method to cluster single cells according to the timing of past transcriptional activity. RNA timestamps will allow the incorporation of temporal information into RNA-seq workflows.