To determine plausible groundwater recharge rates on early Mars, we develop analytic and numerical solutions for an unconfined steady-state aquifer beneath the southern highlands. We show that the aquifer’s mean hydraulic conductivity, $K$, is the primary constraint on the plausible magnitude of mean steady recharge, $r$. By restricting groundwater upwelling to Arabia Terra, using a mean hydraulic conductivity of, $K$ ${\sim}10^{-7}$ m/s, and varying shoreline elevations and recharge distributions, the mean recharge must be order of $10^{-2}$ mm/yr. Recharge for other values of $K$ can be estimated as $r$ ${\sim}10^{-5}\,K$. Our value is near the low end of previous recharge estimates and two orders-of-magnitude below the smallest precipitation estimates. This suggests that, for a steady hydrologic cycle, most precipitation forms runoff, not groundwater recharge. It is also plausible the transient aquifer response to recharge is sufficiently slow that no upwelling occurs prior to cessation of climatic excursions causing precipitation.