Water inventories in Martian magmas are poorly constrained. Meteorite-based estimates range widely, from 102 to >104 ppm H2O, and are likely variably influenced by degassing. Orbital measurements of H primarily reflect water cycled and stored in the regolith. Like water, Th behaves incompatibly during mantle melting, but unlike water Th is not prone to degassing and is relatively immobile during aqueous alteration at low temperature. We employ Th as a proxy for original, mantle-derived H2O in Martian magmas. We use regional maps of Th from Mars Odyssey to assess variations in magmatic water across major volcanic provinces and through time. We infer that Hesperian and Amazonian magmas had ∼100-3,000 ppm H2O, in the lower range of previous estimates. The implied cumulative outgassing since the Hesperian, equivalent to a global H2O layer ∼1-40 m deep, agrees with Mars' present-day surface and near-surface water inventory and estimates of sequestration and loss rates.