Multiferroic structures that provide coupled ferroelectric and ferromagnetic responses are of significant interest as they may be used in novel memory devices and spintronic logic elements. One approach towards this goal is the use of composites that couple ferromagnetic and ferroelectric layers through magnetostrictive and piezoelectric strain transmitted across the interfaces. However, mechanical clamping of the films to the substrate limits their response. Structures where the magnetic response is modulated directly by the electric field of the poled ferroelectric would eliminate this constraint and provide a qualitatively higher level of integration, combining the emerging field of multiferroics with conventional semiconductor microelectronics. Here, we report the realization of such a device using (Ga,Mn)As, which is an archetypical diluted magnetic semiconductor with well-understood carrier-mediated ferromagnetism, and a polymer ferroelectric gate. Polarization reversal of the gate by a single voltage pulse results in a persistent modulation of the Curie temperature of the ferromagnetic semiconductor. The non-volatile gating of (Ga,Mn)As has been made possible by applying a low-temperature copolymer deposition technique that is distinct from pre-existing technologies for ferroelectric gates on magnetic oxides. This accomplishment opens a way to nanometre-scale modulation of magnetic semiconductor properties with rewritable ferroelectric domain patterns, operating at modest voltages and subnanosecond times.