We report the angular dependence of magnetoresistance in the two-dimensional electron gas at the LaAlO3/SrTiO3 interface. We find that this interfacial magnetoresistance exhibits a similar angular dependence to the spin Hall magnetoresistance observed in ferromagnet/heavy metal bilayers, which has been so far discussed in the framework of the bulk spin Hall effect of the heavy metal layer. The observed magnetoresistance is in qualitative agreement with a theoretical model calculation including both Rashba spin-orbit coupling and an exchange interaction. Our result suggests that magnetic interfaces subject to spin-orbit coupling can generate a non-negligible contribution to the spin Hall magnetoresistance, and the interfacial spin-orbit coupling effect is therefore key to the understanding of various spin-orbit-coupling-related phenomena in magnetic/nonmagnetic bilayers.