Inhibitors directed toward PARP1 and PARP2 are approved agents for the treatment of BRCA1 and BRCA2-related cancers. Other members of the PARP family have also been implicated in cancer and are being assessed as therapeutic targets in cancer and other diseases. Recently, an inhibitor of PARP7 (RBN-2397) has reached early-stage human clinical trials. Here, we performed a genome-wide CRISPR screen for genes that modify the response of cells to RBN-2397. We identify the polycyclic aromatic hydrocarbon receptor AHR and multiple components of the cohesin complex as determinants of resistance to this agent. Activators and inhibitors of AHR modulate the cellular response to PARP7 inhibition, suggesting potential combination therapy approaches.