The Cosmic Ray Telescope for the Effects of Radiation (CRaTER) has been orbiting the Moon since 2009 aboard the Lunar Reconnaissance Orbiter (LRO). From this vantage point, it samples the interplanetary energetic particle population outside the shielding of the Earth's magnetosphere. We report the sensor's observations of galactic cosmic rays (GCRs) over a complete solar activity cycle. CRaTER is designed primarily to measure not the spectra of GCR particles outside the sensor but rather their effects on matter, and in particular, it measures the linear energy transfer (LET) or energy‐deposit spectrum in its silicon detectors. We have used the Geant4 radiation‐transport code to devise a background‐rejection algorithm to improve these measurements of LET under 9.9 g/cm2 of shielding, and the resulting observations show the changing radiation effects of GCRs as their intensity and spectrum vary with solar modulation. As of 2020 this intensity, after declining during solar maximum activity, has recovered to a level that exceeds by a few percent the historically high values seen during the deep solar minimum at the start of the LRO mission in 2009.