RNA-protein interactions underlie a wide range of cellular processes. Improved methods are needed to systematically map RNA-protein interactions in living cells in an unbiased manner. Capitalizing on the ability of the engineered peroxidase APEX2 to identify protein interaction partners via proximity-dependent biotinylation, we used two approaches to target APEX2 to specific cellular RNAs. Both an MS2-MCP system and an engineered CRISPR-Cas13 system were able to deliver APEX2 to the human telomerase RNA hTR with high specificity. One-minute proximity biotinylation captured endogenous protein interaction partners of hTR, including more than a dozen proteins not previously linked to hTR. We validated the unexpected interaction between hTR and the N6-methyladenosine (m6A) demethylase ALKBH5. Further investigation showed that endogenous hTR is modified by m6A, which can be erased by ALKBH5, and that ALKBH5 influences both telomerase complex assembly and activity. These results highlight the ability of MS2- and Cas13-targeted APEX2 to identify novel RNA-protein interactions in living cells.