We report on the circular and linear photogalvanic effects caused by free-carrier absorption of terahertz radiation in electron channels on (001)-oriented and miscut silicon surfaces. The photocurrent behaviour upon variation of the radiation polarization state, wavelength, gate voltage, and temperature is studied. We present the microscopic and phenomenological theory of the photogalvanic effects, which describes well the experimental results. In particular, it is demonstrated that the circular (photon-helicity sensitive) photocurrent in silicon-based structures is of pure orbital nature originating from the quantum interference of different pathways contributing to the absorption of monochromatic radiation.