A new mechanism has recently been proposed that generates a radial flux of parallel momentum in toroidal plasmas. Namely, by considering up-down asymmetric flux surfaces, the symmetry following the magnetic field can be broken and an additional contribution to the turbulent momentum flux arises, potentially changing the intrinsic rotation profile. These predictions are tested with specific experiments on TCV. The intrinsic toroidal rotation is observed to change by roughly a factor of two when changing the up-down asymmetry of the plasma. More precisely, the toroidal rotation gradient changes in the outer part of the plasma, where the flux surface asymmetry is the highest. The experiments were performed for all combinations of the toroidal magnetic field and plasma current directions, that affect the sign of the predicted up-down asymmetry flux. In each case the variation of the intrinsic rotation profile with the up-down asymmetry is observed in the direction predicted by the theory.