Certain environmental toxins and chemotherapeutics are nucleic acid-damaging agents, causing adducts in DNA and RNA. While most of these adducts occur in RNA, the consequences of RNA damage are largely unexplored. Here, we demonstrate that nuclear RNA damage can result in loss of genome integrity in human cells. Specifically, we show that YTHDC1 regulates alkylation damage responses with the THO complex (THOC). In addition to its established binding to N6-methyladenosine (m(6)A), YTHDC1 binds to chemically induced N1-methyladenosine (m(1)A). Without YTHDC1, cells have greater alkylation damage sensitivity and increased DNA breaks, which are rescued by an RNA-specific dealkylase. These RNA-damage-induced DNA breaks (RDIBs) depend on R-loop formation, which is converted to DNA breaks by the XPG nuclease. Strikingly, in the absence of YTHDC1 or THOC, a nuclear RNA m(1)A methyltransferase is sufficient to induce DNA breaks. Our results provide mechanistic insight into how damaged RNAs can impact genomic integrity.