Mars’ polar layered deposits record critical information about its climate history. Here, I numerically model formation of alternating layers of CO2 and H2O ice in Mars’ south polar Massive CO2 Ice Deposit to reconstruct its H2O ice depositional history over the past 510 thousand years. Statistical analyses of ~10^9 model runs favor a best-fit historical H2O ice deposition function that exponentially decreases with obliquity, with ~1, 0.1, and 0.01 mm yr^-1 rates for 20, 24, and 28 deg. obliquity, respectively. Recovery of a south polar H2O-ice-deposition-versus-obliquity function is novel and important for elucidating Mars’ global water cycle; previous south polar layer analyses were limited to calculation of net average deposition rates over millions of years.