  In this letter a pinch velocity of toroidal momentum is shown to exist for
the first time. Using the gyro-kinetic equations in the frame moving with the
equilibrium toroidal velocity, it is shown that the physics effect can be
elegantly formulated through the ``Coriolis'' drift. A fluid model is used to
highlight the main coupling mechanisms between the density and temperature
perturbations on the one hand and the perturbed parallel flow on the other.
Gyro-kinetic calculations are used to accurately asses the magnitude of the
pinch. The pinch velocity leads to a radial gradient of the toroidal velocity
profile even in the absence of a torque on the plasma. It is shown to be
sizeable in the plasmas of the International Thermonuclear Experimental Reactor
(ITER) leading to a moderately peaked rotation profile. Finally, the pinch also
affects the interpretation of current experiments.
