Impurity toroidal rotation has been observed in the centre of Alcator C-Mod ion cyclotron range of frequencies (ICRF) heated plasmas, from the Doppler shifts of argon X ray lines. Rotation velocities greater than 1.2 × 107 cm/s (ω = 200 krad/s) in the co-current direction have been observed in H mode discharges that had no direct momentum input. There is a correlation between the increase in the central impurity rotation velocity and the increase in the plasma stored energy (confinement enhancement), induced by ICRF heating, although other factors may be at play. The toroidal rotation velocity is highest near the magnetic axis, and decreases with increasing minor radius. A radial electric field of 300 V/cm at r/a = 0.3 has been inferred from the force balance equation. The direction of the rotation changes when the plasma current direction is reversed, remaining co-current. Impurity toroidal rotation in ICRF heated plasmas is in the direction opposite to the rotation in ohmic L mode plasmas; co-current rotation has also been observed during purely ohmic H modes. When the ICRF heating is turned off, the toroidal rotation decays with a characteristic time of order 50 ms, similar to the energy confinement time, and much shorter than the calculated neoclassical momentum damping time.