The spin-polarized electron transport through a three-terminal three-arm ring with two quantum dots separately embedded in the upper and lower arms were theoretically studied. The intradot Coulomb interaction on the two dots and the Rashba spin-orbit interaction inside one arm of the ring were taken into account. With the aid of the nonequilibrium Greens function method,we find that even without using any magnetic factors a Rashba induced spin interference effect can drive a spin-polarized current out of the device. By properly tuning the system parameters such as the applied external voltages,the Rashba interaction strength and the dot levels,not only a fully spin-polarized current but also a pure spin current can be obtained. Moreover,the effects of the system parameters on the magnitude, sign, spin-polarization and resonant peaks of the spin-polarized current were also discussed.