Theories of gravity with torsion indicate that spin-torsion coupling impacts the propagation of spin particles in a torsion field background. This paper encompasses the Dirac action in a curved spacetime with torsion, generalized geometrical hydrodynamics method from the flat Riemann spacetime to Robertson-Walker spacetime, and obtained semiclassical equations including the flow conservation equation, dynamic equation, and spin evolution equation, which describe the behavior of a spin 1/2 particle in arbitrary curved spacetime with torsion. These equations show that spin-torsion interaction usually causes the particles to deviate from the geodesic. Moreover, a solution for the cosmological background is found with definitive cosmological torsion; it concludes that the motion of the particle under the torsion field is a spiral motion along the propagation path, which the particle would take without torsion. This effect, subsequently, verifies the cosmological models established on theories of gravity with torsion.