The Radiation Assessment Detector onboard the Mars Science Laboratory rover Curiosity is detecting the energetic particle radiation at the surface of Mars. Data collected over the first 350 Martian days of the nominal surface mission show a pronounced diurnal cycle in both the total dose rate and the neutral particle count rate. The diurnal variations detected by the Radiation Assessment Detector were neither anticipated nor previously considered in the literature. These cyclic variations in dose rate and count rate are shown to be the result of changes in atmospheric column mass driven by the atmospheric thermal tide that is characterized through pressure measurements obtained by the Rover Environmental Monitoring Station, also onboard the rover. In addition to bulk changes in the radiation environment, changes in atmospheric shielding forced by the thermal tide are shown to disproportionately affect heavy ions compared to H and He nuclei.