We report proximity effects of spin-orbit coupling in EuO$_{1-x}$ films capped with a Pt overlayer. Transport measurements suggest that current flows along a conducting channel at the interface between the Pt and EuO. The temperature dependence of the resistivity picks up the critical behaviors of EuO, i.e., the metal-to-insulator transition. We also find an unusual enhancement of the magnetic anisotropy in this structure from its bulk value which results from strong spin-orbit coupling across the Pt/EuO interface.