Andreev reflection (AR) in ferromagnet/superconductor junctions is an indispensable spectroscopic tool for measuring spin polarization. We study theoretically how the presence of a thin semiconducting interface in such
junctions, inducing Rashba and Dresselhaus spin-orbit coupling, modifies AR processes. The interface gives rise to a momentum- and spin-dependent scattering potential, making the AR probability strongly asymmetric with
respect to the sign of the incident electrons’ transverse momenta. This skew AR creates spatial charge carrier imbalances and transverse Hall currents in the ferromagnet. We show that the effect is giant, compared to the normal regime. We provide a quantitative analysis and a qualitative picture of this phenomenon, and finally show that skew AR also leads to a widely tunable transverse supercurrent response in the superconductor.