We report on the study of spin-polarized electric currents in diluted magnetic semiconductor (DMS) quantum wells subjected to an in-plane external magnetic field and illuminated by microwave or terahertz radiation. The effect is studied in (Cd, Mn)Te/(Cd, Mg)Te quantum-wells (QWs) and (In, Ga)As/InAlAs:Mn QWs belonging to the well-known II-VI and III-V DMS material systems, as well as in heterovalent AlSb/InAs/(Zn,Mn) Te QWs, which represent a promising combination of II-VI and III-V semiconductors. Experimental data and developed theory demonstrate that the photocurrent originates from a spin-dependent scattering of free carriers by static defects or phonons in the Drude absorption of radiation and subsequent relaxation of carriers. We show that in DMS structures, the efficiency of the current generation is drastically enhanced compared to nonmagnetic semiconductors. The enhancement is caused by the exchange interaction of carrier spins with localized spins of magnetic ions resulting, on the one hand, in the giant Zeeman spin splitting, and, on the other hand, in the spin-dependent carrier scattering by localized Mn2+ ions polarized by an external magnetic field.