Rapid progress in nanofabrication methods has fuelled a quest for ultra-compact photonic integrated systems and nanoscale light sources. The prospect of small-footprint, high-quality emitters of short-wavelength radiation is especially exciting due to the importance of extreme-ultraviolet and X-ray radiation as research and diagnostic tools in medicine, engineering and the natural sciences. Here, we propose a highly directional, tunable and monochromatic radiation source based on electrons interacting with graphene plasmons. Our complementary analytical theory and ab initio simulations demonstrate that the high momentum of the strongly confined graphene plasmons enables the generation of high-frequency radiation from relatively low-energy electrons, bypassing the need for lengthy electron acceleration stages or extreme laser intensities. For instance, highly directional 20 keV photons could be generated in a table-top design using electrons from conventional radiofrequency electron guns. The conductive nature and high damage threshold of graphene make it especially suitable for this application. Our electron-plasmon scattering theory is readily extended to other systems in which free electrons interact with surface waves.