The two-dimensional superconductor that forms at the interface between the complex oxides lanthanum aluminate (LAO) and strontium titanate (STO) has several intriguing properties that set it apart from conventional superconductors. Most notably, an electric field can be used to tune its critical temperature (Tc; ref. 7), revealing a dome-shaped phase diagram reminiscent of high-Tc superconductors. So far, experiments with oxide interfaces have measured quantities that probe only the magnitude of the superconducting order parameter and are not sensitive to its phase. Here, we perform phase-sensitive measurements by realizing the first superconducting quantum interference devices (SQUIDs) at the LAO/STO interface. Furthermore, we develop a new paradigm for the creation of superconducting circuit elements, where local gates enable the in situ creation and control of Josephson junctions. These gate-defined SQUIDs are unique in that the entire device is made from a single superconductor with purely electrostatic interfaces between the superconducting reservoir and the weak link. We complement our experiments with numerical simulations and show that the low superfluid density of this interfacial superconductor results in a large, gate-controllable kinetic inductance of the SQUID. Our observation of robust quantum interference opens up a new pathway to understanding the nature of superconductivity at oxide interfaces.