  We study directed transport of charge and intrinsic angular momentum by
periodically driven scattering in the regime of fast and strong driving. A
spin-orbit coupling through a kicked magnetic field confined to a compact
region in space leads to irregular scattering and triggers spin flips in a
spatially asymmetric manner which allows to generate polarized currents. The
dynamical mechanisms responsible for the spin separation carry over to the
quantum level and give rise to spin pumping. Our theory, based on the Floquet
formalism, is confirmed by numerical solutions of the time-dependent
inhomogeneous Schr\"{o}dinger equation with a continuous source term.
