X-ray microscopy offers the opportunity to image biological and radiosensitive materials without special sample preparations, bridging optical and electron microscopy capabilities. However, the performance of such microscopes, when imaging radiosensitive samples, is not limited by their intrinsic resolution, but by the radiation damage induced on such samples. Here, we demonstrate a novel, to the best of our knowledge, radio-efficient microscope, scanning Compton X-ray microscopy (SCXM), which uses coherently and incoherently (Compton) scattered photons to minimize the deposited energy per unit of mass for a given imaging signal. We implemented SCXM, using lenses capable of efficiently focusing 60 keV X-ray photons into the sub-micrometer scale, and probe its radio-efficient capabilities. SCXM, when implemented in high-energy diffraction-limited storage rings, e.g., European Synchrotron Radiation Facility Extremely Brilliant Source and PETRA IV, will open the opportunity to explore the nanoscale of unstained, unsectioned, and undamaged radiosensitive materials.