The equilibrium plasma rotation in a general toroidal magnetic field is nearly always subsonic and is determined by the requirement that the collisional particle transport should be ambipolar in lowest order in the small-ion-gyroradius expansion. Only in quasi-symmetric fields, where collisional particle transport is intrinsically ambipolar, can the plasma rotate freely and then only in the quasi-symmetry direction. Sonic rotation velocities are allowed in this case. In this paper the effect of rotation in a quasi-axisymmetric field is investigated, and it is found that the symmetry is broken when the rotation speed exceeds the diamagnetic speed appreciably, leading to reappearance of the non-intrinsically ambipolar 1/ν-transport regime. Fortunately, this transport scales with the fourth power of the rotation Mach number and is expected to be modest in most plasmas of interest.