We demonstrate that a symmetry of the local gyrokinetic model is broken when the safety factor is almost (but not exactly) a rational number and magnetic shear is . Tokamaks with such a profile will spontaneously rotate due to turbulent momentum transport. Nonlinear gyrokinetic simulations indicate this mechanism is significantly stronger than all other drives of intrinsic rotation. It also intrinsically transports electric current, pulling towards rational values and potentially aiding non-inductive current drive. This is likely important in the triggering of internal transport barriers.