The spin-splitting energy bands induced by the relativistic spin-orbit interaction in solids provide a new opportunity to manipulate the spin-polarized electrons on the sub-picosecond time scale. Here, we report one such example in a bulk Rashba-type polar semiconductor BiTeBr. Strong terahertz electromagnetic waves are emitted after the resonant excitation of the interband transition between the Rashba-type spin-splitting energy bands with a femtosecond laser pulse circularly polarized. The phase of the emitted terahertz waves is reversed by switching the circular polarization. This suggests that the observed terahertz radiation originates from the subpicosecond spin-polarized photocurrents, which are generated by the asymmetric depopulation of the Dirac state. Our result provides a new way for the current-induced terahertz radiation and its phase control by the circular polarization of incident light without external electric fields.