A new method for generating spin-polarized currents in topological insulators has been proposed and investigated. The method is associated with the spin-dependent asymmetry of the generation of holes at the Fermi level for branches of topological surface states with the opposite spin orientation under the circularly polarized synchrotron radiation. The result of the generation of holes is the formation of compensating spin-polarized currents, the value of which is determined by the concentration of the generated holes and depends on the specific features of the electronic and spin structures of the system. The indicator of the formed spin-polarized current can be a shift of the Fermi edge in the photoelectron spectra upon photoexcitation by synchrotron radiation with the opposite circular polarization. The topological insulators with different stoichiometric compositions (Bi_1.5Sb_0.5Te_1.8Se_1.2 and PbBi₂Se₂Te₂) have been investigated. It has been found that there is a correlation in the shifts and generated spin-polarized currents with the specific features of the electronic spin structure. Investigations of the graphene/Pt(111) system have demonstrated the possibility of using this method for other systems with a spin-polarized electronic structure.