We predict that vertical transport in heterostructures formed by twisted graphene layers can exhibit a unique bistability mechanism. Intrinsically bistable $I$-$V$ characteristics arise from resonant tunneling and interlayer charge coupling, enabling multiple stable states in the sequential tunneling regime. We consider a simple trilayer architecture, with the outer layers acting as the source and drain and the middle layer floating. Under bias, the middle layer can be either resonant or non-resonant with the source and drain layers. The bistability is controlled by geometric device parameters easily tunable in experiments. The nanoscale architecture can enable uniquely fast switching times.