In this Letter, we report on the circular anisotropy of third-harmonic (TH) generation in an array of silicon nanowires (SiNWs) of approximately 100 nm in diameter tilted to the crystalline silicon substrate at an angle of 45°. Numerical simulations of the scattering at the fundamental and TH frequencies of circularly polarized light by a single SiNW and an ansatz structure composed of 13 SiNWs used as a geometrical approximation of the real SiNW array indicate asymmetric scattering diagrams, which is a manifestation of the photonic spin Hall effect mediated by the synthetic gauge field arising due to the special guided-like mode structure in each SiNW. Despite strong light scattering in the SiNW array, the experimentally measured TH signal demonstrated significant dependence on the polarization state of incident radiation and the SiNW array spacial orientation in regard to the wave vector direction.