We describe the initial implementation of magnetohydrodynamics (MHD) in our astrophysical simulation code genasis. Then, we present MHD simulations exploring the capacity of the stationary accretion shock instability (SASI) to generate magnetic fields by adding a weak magnetic field to an initially spherically symmetric fluid configuration that models a stalled shock in the post-bounce supernova environment. Upon perturbation and nonlinear SASI development, shear flows associated with the spiral SASI mode contributes to a widespread and turbulent field amplification mechanism. While the SASI may contribute to neutron star magnetization, these simulations do not show qualitatively new features in the global evolution of the shock as a result of SASI-induced magnetic field amplification.