The two-dimensional electron system (2DES) formed at the interface of LaAlO3 (LAO) and SrTiO3 (STO), both band insulators in bulk, exhibits properties not easily attainable in conventional electronic materials. The extreme shallowness of the 2DES, only a few nanometers below the surface, opens up unique possibilities such as tunneling spectroscopy, local electronic sensing, and in situ patterning by manipulating the surface properties. It is particularly tempting to manipulate the charge carriers with surface acoustic wave (SAW) phonons, which are confined to the surface. However, the absence of intrinsic piezoelectricity in both LAO and STO complicates the electric generation of SAWs, as well as the induction of an acoustoelectric current. Here, we present robust acoustoelectric coupling between SAWs and the LAO/STO 2DES by using electrostriction in STO, induced by a dc electric field. Electromechanical coupling to the carriers is provided by phonon-induced modulation of the 2DES potential well, leading to SAW-induced carrier transport. The ability to control charge carriers with SAWs brings the versatile LAO/STO 2DES into reach of quantum acoustics, opening possibilities to study the interplay of nanoscale mechanical waves and the rich physics exhibited by nonpiezoelectric complex oxides, including superconductivity, magnetism, and correlated insulator states.