We demonstrate that the combined effect of a spatially periodic potential, lateral confinement, and spin-orbit interaction gives rise to a quantum ratchet mechanism for spin-polarized currents in two-dimensional coherent conductors. Upon adiabatic ac driving, in the absence of a net static bias, the system generates a directed spin current while the total charge current is zero. We analyze the underlying mechanism by employing symmetry properties of the scattering matrix and numerically verify the effect for different setups of ballistic conductors. The spin current direction can be changed upon tuning the Fermi energy or the strength of the Rashba spin-orbit coupling.