CRISPR-Cas base-editor technology enables targeted nucleotide alterations， and is being increasingly used for research and potential therapeutic applications. The most widely used cytosine base editors (CBEs) induce deamination of DNA cytosines using the rat APOBEC1 enzyme， which is targeted by a linked Cas protein-guide RNA complex. Previous studies of the specificity of CBEs have identified off-target DNA edits in mammalian cells. Here we show that a CBE with rat APOBEC1 can cause extensive transcriptome-wide deamination of RNA cytosines in human cells， inducing tens of thousands of C-to-U edits with frequencies ranging from 0.07% to 100% in 38-58% of expressed genes. CBE-induced RNA edits occur in both protein-coding and non-protein-coding sequences and generate missense， nonsense， splice site， and 5' and 3' untranslated region mutations. We engineered two CBE variants bearing mutations in rat APOBEC1 that substantially decreased the number of RNA edits (by more than 390-fold and more than 3，800-fold) in human cells. These variants also showed more precise on-target DNA editing than the wild-type CBE and， for most guide RNAs tested， no substantial reduction in editing efficiency. Finally， we show that an adenine base editor can also induce transcriptome-wide RNA edits. These results have implications for the use of base editors in both research and clinical settings， illustrate the feasibility of engineering improved variants with reduced RNA editing activities， and suggest the need to more fully define and characterize the RNA off-target effects of deaminase enzymes in base editor platforms.