The polarization direction of a ferroelectric-like state can be used to control the conversion of spin currents into charge currents at the surface of strontium titanate, a non-magnetic oxide. After 50 years of development, the technology of today's electronics is approaching its physical limits, with feature sizes smaller than 10 nanometres. It is also becoming clear that the ever-increasing power consumption of information and communication systems(1) needs to be contained. These two factors require the introduction of non-traditional materials and state variables. As recently highlighted(2), the remanence associated with collective switching in ferroic systems is an appealing way to reduce power consumption. A promising approach is spintronics, which relies on ferromagnets to provide non-volatility and to generate and detect spin currents(3). However, magnetization reversal by spin transfer torques(4) is a power-consuming process. This is driving research on multiferroics to achieve low-power electric-field control of magnetization(5), but practical materials are scarce and magnetoelectric switching remains difficult to control. Here we demonstrate an alternative strategy to achieve low-power spin detection, in a non-magnetic system. We harness the electric-field-induced ferroelectric-like state of strontium titanate (SrTiO3)(6-9) to manipulate the spin-orbit properties(10) of a two-dimensional electron gas(11), and efficiently convert spin currents into positive or negative charge currents, depending on the polarization direction. This non-volatile effect opens the way to the electric-field control of spin currents and to ultralow-power spintronics, in which non-volatility would be provided by ferroelectricity rather than by ferromagnetism.