Spin–orbit torques enable energy-efficient manipulation of magnetization by electric current and hold promise for applications ranging from non-volatile memory to neuromorphic computing. Here the discovery of a giant spin–orbit torque induced by anomalous Hall current in ferromagnetic conductors is reported. This anomalous Hall torque is self-generated as it acts on the magnetization of the ferromagnet that engenders the torque. The magnitude of the anomalous Hall torque is sufficiently large to fully negate magnetic damping of the ferromagnet, which allows implementation of a microwave spin torque nano-oscillator driven by this torque. The peculiar angular symmetry of the anomalous Hall torque favors its use over the conventional spin Hall torque in coupled nano-oscillator arrays. The universal character of the anomalous Hall torque makes it an integral part of the description of coupled spin transport and magnetization dynamics in magnetic nanostructures.