In spin torque magnetic memories, electrically actuated spin currents are used to switch a magnetic bit. Typically, these require a multilayer geometry including both a free ferromagnetic layer and a second layer providing spin injection. For example, spin may be injected by a non-magnetic layer exhibiting a large spin Hall effect, a phenomenon known as spin–orbit torque. Here we demonstrate a spin–orbit torque magnetic bit in a single two-dimensional system with intrinsic magnetism and strong Berry curvature. We study AB-stacked MoTe2/WSe2, which hosts a magnetic Chern insulator at a carrier density of one hole per moiré superlattice site. We observe hysteretic switching of the resistivity as a function of applied current. Magnetic imaging reveals that current switches correspond to reversals of individual magnetic domains. The real space pattern of domain reversals aligns with spin accumulation measured near the Hubbard band edges with high Berry curvature. This suggests that intrinsic spin or valley Hall torques drive the observed current-driven magnetic switching in both MoTe2/WSe2 and other moiré materials. The switching current density is substantially less than those reported in other platforms, suggesting that moiré heterostructures are a suitable platform for efficient control of magnetic order. © 2023, The Author(s), under exclusive licence to Springer Nature Limited.