The magnetic field dependence of the capacitance of Pd-AlOx-Al thin-film structures has been measured. The observed quadratic dependence of capacitance on the magnetic field is consistent with a theoretical model that includes the effect of a spin-dependent electrochemical potential on electron screening in the paramagnetic Pd. This spin-dependent electrochemical potential is related to the Zeeman splitting of the narrow d bands in Pd. The quantitative details depend on the electronic band structure at the surface of Pd.