High-latitude ground ice on Mars discovered by the Gamma Ray Spectrometer suite is thought to be thermally stable owing to the presence of vapor in the Martian atmosphere. However, local slopes can alter surface and subsurface temperatures substantially, and hence allow ground ice to persist at locations where it would otherwise be unstable. Global statistics of the topography of Mars are computed, processed, and extrapolated to derive a description of surface roughness on spatial scales to which ground ice should be sensitive. This slope distribution is convolved with a new thermal model for the dependence of subsurface ice on slope, to produce a prediction of the global ice distribution that includes the effect of topographic roughness. In the highest latitudes, slopes reduce the amount of buried ice, while in lower latitudes the ice fraction increases, widening the geographic boundary of the ice table. At the high latitudes, where ice is stable beneath horizontal ground, the estimated reduction of ice is small compared to the existing ice volume. Areas in the midlatitudes with high surface roughness that have previously been predicted to be ice free are predicted to contain quantities of ice that may be detectable at present and accessible in the future. Slopes cause ground ice to be stable to latitudes of about 25 degrees in both hemispheres, including, for example, areas within the northern Olympus Mons aureole deposits, Hecates Tholus, and Hellas basin. Ice is unstable at equatorial latitudes, even when accounting for surface slopes.