The injection of LH waves for current drive into a tokamak changes the ion toroidal rotation. In Alcator C-Mod, the direction of the steady state rotation change due to LH waves depends on the plasma current and the density. The change in rotation can be estimated by balancing the external torque of lower hybrid waves with the turbulent radial transport of the momentum. For high plasma current, the turbulent pinch and diffusion of the injected counter-current momentum are sufficient to explain the rotation change. However, for low plasma current, the change in the the intrinsic momentum transport (residual stress) for a non-rotating state is required to explain the co-current rotation change. Accordingly, we investigate the intrinsic momentum transport for the non-rotating state when diamagnetic flow and ExB flow cancel each other. The change in the intrinsic momentum transport due to lower hybrid waves is significant when the plasma current is low, which may explain the rotation reversal for low plasma current. The effect of changed q (safety factor) profile by lower hybrid on the intrinsic momentum transport is estimated by gyrokinetics.