We observed on-off intermittency in the chaotic rotation induced by a cw laser beam in a thin liquid crystal film where the spin and the orbital angular momentum of light compete in reorienting the sample. We found that the azimuthal angle phi(t) of the molecular director increased linearly in time on large time scales but, occasionally, it exhibited large fluctuations about its average value omega(0)t, so that its angular velocity phi;(t) undergoes an on-off intermittent motion. The intermittent signal omega(t)=phi;(t)-omega(0) obeyed the scaling laws of on-off intermittency, including the symmetry between laminar and burst phases. The chaotic rotations were observed only when the spin and the angular momentum of light were transferred simultaneously to the sample.