A kinetic model for ion turbulent parallel momentum transport is developed with finite orbit width effects for Tokamak plasmas. It is shown that the curvature and gradient drifts of ions can introduce pressure perturbations into the transport equation of ion parallel momentum, which leads to a new source term. And the source term can be understood as a Coriolis force and can play a key role in the toroidal symmetry breaking during the spontaneous spin-up process.