By means of angle- and spin-resolved photoemission, we demonstrate a possibility of the out-of-plane spin polarization of topological surface states and corresponding lifting of the Kramers degeneracy at the Dirac point induced in magnetically-doped topological insulator Bi_1.37V_0.03Sb_0.6Te₂Se by circularly polarized synchrotron radiation (SR) at room temperature. It has been shown that the induced out-of-plane polarization is created due to an "optically"-generated uncompensated spin accumulation with transferring the induced torque to the diluted V 3d ions. We have found theoretically a relation between the imbalance in depopulation of the Dirac cone states under photoexcitation, the generation of steady-state uncompensated spin accumulation and the induced magnetization that can be managed by the polarization of SR.