Realizing programmable topological states in quantum anomalous Hall (QAH) insulators requires tuning their topological invariant, the Chern number C. Here we report a QAH platform based on twisted rhombohedral graphene, in which C becomes a programmable and electrically tunable degree of freedom. In twisted monolayer–multilayer (1 + N) rhombohedral graphene, we find QAH states with C = N, where the layer number N = 3, 4, 5 directly sets the Chern number. We further demonstrate in situ electrical control. In a twisted monolayer–trilayer device, the sign of C is switched by electrostatic doping or displacement field. In addition, in twisted Bernal bilayer–rhombohedral tetralayer graphene, we drive a displacement-field-induced topological phase transition between two distinct QAH states with C = 3 and C = 4. Our work establishes a layer-engineered and electrically tunable platform that could lead to the on-demand engineering of correlated topological states.