The rotation of a toroidally confined plasma about its magnetic axis due to resistive diffusion is studied by means of a single fluid model in which the only dissipation occurs through a small scalar resistivity. The time evolution of the rotation is examined by considering the resistivity as inducing first‐order time variation on a dissipationless steady state. The known instability of flows with small rotational velocity to rapidly speed up toward a critical speed is confirmed; more importantly, it is found that a shock which develops at the critical speed stabilizes the flow, so that the ultimate state of the system is characterized by steady rotation with a very weak shock front directed radially inward from the magnetic axis. The outward flux of plasma in this state is found to be essentially the Pfirsch‐Schlu¨ter flux enhanced by a factor of the square root of the aspect ratio.