The tilted-foil method for producing spin-polarized radioactive isotope beams has been studied using the re-accelerated radioactive 8Li and 123In beams produced at Tokai Radioactive Ion Accelerator Complex (TRIAC) facility. We successfully produced polarization in a 8Li beam of 7.3(5)% using thin polystyrene foils (4.2μg/cm2). The systematic study of the nuclear polarization as a function of the number of foils and beam energy has been performed, confirming the features of the tilted-foil technique experimentally. After the study, a spin-polarized radioactive 123In beam, which is the heaviest ever polarized in its ground state by this method, has been successfully generated by the tilted-foil method, for the nuclear spectroscopy around the doubly magic nucleus 132Sn.