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We demonstrate gate voltage control of the critical current of a surface channel of the low-carrier-density, bulk-superconducting oxide system SrTiO₃. The devices are in a conventional field effect transistor geometry with a solid gate dielectric and superconducting leads. We can modulate the critical current by a factor of 2-3 in our devices as a function of gate voltage. Additionally, we study the magnetic field dependence of the differential resistance of these devices to understand the role the superconducting leads play on the channel properties. A device such as this could serve as a new qubit architecture when integrated into a microwave resonator circuit.