  The ion toroidal rotation in a tokamak consists of an $E\times B$ flow due to
the radial electric field and a diamagnetic flow due to the radial pressure
gradient. The turbulent pinch of toroidal angular momentum due to the Coriolis
force studied in previous work is only applicable to the $E\times B$ flow. In
this Letter, the momentum pinch for the rotation generated by the radial
pressure gradient is calculated and is compared with the Coriolis pinch. This
distinction is important for subsonic flows or the flow in the pedestal where
the two types of flows are similar in size and opposite in direction. In the
edge, the different pinches due to the opposite rotations can result in
intrinsic momentum transport that gives significant rotation peaking.
