Possibility of in-plane and out-of-plane magnetization generated by synchrotron radiation (SR) in magnetically doped and pristine topological insulators (TIs) is demonstrated and studied by angle-resolved photoemission spectroscopy. We show experimentally and by ab initio calculations how nonequal depopulation of the Dirac cone (DC) states with opposite momenta in V-doped and pristine TIs generated by linearly polarized SR leads to the hole-generated uncompensated spin accumulation followed by the SR-induced magnetization via spin-torque effect. Moreover, the photoexcitation of the DC is asymmetric, and it varies with the photon energy. We find a relation between the photoexcitation asymmetry, the generated spin accumulation, and the induced in-plane and out-of-plane magnetic field. Experimentally the SR-generated in-plane and out-of-plane magnetization is confirmed by the k shift of the DC position and by the gap opening at the Dirac point even above the Curie temperature. Theoretical predictions and estimations of the measurable physical quantities substantiate the experimental results.