Central impurity toroidal rotation has been observed in Alcator C-Mod ICRF heated plasmas, from the Doppler shifts of argon X ray lines. Rotation velocities of up to 1.3 x 10(5) m/s in the co-current direction have been observed in H mode discharges with no direct momentum input. There is a strong correlation between the increase in the central impurity rotation velocity and the increase in the plasma stored energy, induced by ICRF heating, although other factors may be involved. This implies a close association between energy and momentum confinement. Go-current rotation is also observed during purely ohmic H modes. In otherwise similar discharges with the same stored energy increase, plasmas with lower current rotate faster. For hydrogen minority (D(H)) heating, plasmas with the highest rotation have an H/D ratio between 5 and 10% and have the resonance location in the inner half of the plasma, i.e. in the same conditions that are conducive to the best ICRF absorption and heating. Comparisons with neoclassical theory indicate that the ion pressure gradient is an unimportant contributor to the central impurity rotation and the presence of a substantial core radial electric field is inferred during the ICRF pulse. An inward shift of ions induced by ICRF waves could give rise to a non-ambipolar electric field in the plasma core.