The microscopic structure of spin-orbit fields for the technologically important Fe/GaAs interface is uncovered from first principles. A symmetry based method allows us to obtain the spin-orbit fields-both their magnitude and orientation-for a generic Bloch state, from the electronic band structure for any in-plane magnetization orientation. It is demonstrated that the spin-orbit fields depend not only on the electric field across the interface, but also surprisingly strongly on the Fe magnetization orientation, opening prospects for their magnetic control. These results give important clues in searching for spin-orbit transport and optical phenomena in ferromagnet/nonmagnet heterostructures.