We theoretically investigate spin transport in the elliptical ring and the circular ring with Rashba spin-orbit interaction. It is shown that when Rashba spin-orbit interaction is relatively weak, a single circular ring can not realize spin flip, however an elliptical ring may work as a spin-inverter at this time, and the influence of the defect of the geometry is not obvious. Howerver if a giant Rashba spin-orbit interaction strength has been obtained, a circular ring can work as a spin-inverter with a high stability.