The magneto-gyrotropic photogalvanic and spin-galvanic effects are observed in (0001)-oriented GaN/AlGaN heterojunctions excited by terahertz radiation. We show that free-carrier absorption of linearly or circularly polarized terahertz radiation in low-dimensional structures causes an electric photocurrent in the presence of an in-plane magnetic field. Microscopic mechanisms of these photocurrents based on spin-related phenomena are discussed. Properties of the magneto-gyrotropic and spin-galvanic effects specific for hexagonal heterostructures are analyzed.