Radial velocity monitoring has found the signature of a Msini = 1.3M⊕ planet located within the habitable zone (HZ) of Proxima Centauri. Despite a hotter past and an active host star, the planet Proxima b could have retained enough volatiles to sustain surface habitability. Here we use a 3D Global Climate Model (GCM) to simulate the atmosphere and water cycle of Proxima b for its two likely rotation modes (1:1 and 3:2 spin-orbit resonances), while varying the unconstrained surface water inventory and atmospheric greenhouse effect. Any low-obliquity, low-eccentricity planet within the HZ of its star should be in one of the climate regimes discussed here. We find that a broad range of atmospheric compositions allow surface liquid water. On a ...