Quantum materials are characterized by electromagnetic responses intrinsically linked to the geometry and topology of electronic wavefunctions that are encoded in the quantum metric and Berry curvature. Whereas Berry curvature-mediated transport effects have been identified in several magnetic and nonmagnetic systems, quantum metric-induced transport phenomena remain limited to topological antiferromagnets. Here, we show that spin-momentum locking, a general characteristic of the electronic states at surfaces and interfaces of spin-orbit-coupled materials, leads to a finite quantum metric. This metric activates a nonlinear in-plane magnetoresistance that we measured and electrically controlled in 111-oriented LaAlO₃ /SrTiO₃ interfaces. These findings demonstrate the existence of quantum metric effects in a vast class of materials and enable previously unexplored strategies to design functionalities based on quantum geometry.