The error-free and efficient repair of DNA double-stranded breaks (DSBs) is extremely important for cell survival. RNA has been implicated in the resolution of DNA damage but the mechanism remains poorly understood. Here, we show that miRNA biogenesis enzymes, Drosha and Dicer, control the recruitment of repair factors from multiple pathways to sites of damage. Depletion of Drosha significantly reduces DNA repair by both homologous recombination (HR) and non-homologous end joining (NHEJ). Drosha is required within minutes of break induction, suggesting a central and early role for RNA processing in DNA repair. Sequencing of DNA:RNA hybrids reveals RNA invasion around DNA break sites in a Drosha-dependent manner. Removal of the RNA component of these structures results in impaired repair. These results show how RNA can be a direct and critical mediator of DNA damage repair in human cells.