An electric current in the presence of spin-orbit coupling can generate a spin accumulation that exerts torques on a nearby magnetization. We demonstrate that, even in the absence of materials with strong bulk spin-orbit coupling, a torque can arise solely due to interfacial spin-orbit coupling, namely, Rashba-Eldestein effects at metal/insulator interfaces. In magnetically soft NiFe sandwiched between a weak spin-orbit metal (Ti) and insulator (Al2O3), this torque appears as an effective field, which is significantly larger than the Oersted field and qualitatively modified by inserting an additional layer between NiFe and Al2O3. Our findings point to unconventional routes for tuning spin-orbit torques by engineering interfacial electric dipoles.