Optically induced mechanical torque driving rotation of small objects requires the presence of absorption or breaking cylindrical symmetry of a scatterer. A spherical nonabsorbing particle cannot rotate due to the conservation of the angular momentum of light upon scattering. Here, we suggest a novel physical mechanism for the angular momentum transfer to nonabsorbing particles via nonlinear light scattering. The breaking of symmetry occurs at the microscopic level manifested in nonlinear negative optical torque due to the excitation of resonant states at the harmonic frequency with higher projection of angular momentum. The proposed physical mechanism can be verified with resonant dielectric nanostructures, and we suggest some specific realizations.