We investigate the conductance of an open quantum dot in which uniform Rashba spin-orbit interaction ( SOI) is present in the cavity region. The dot has a central triangular stopper ( CTS) whose rotation angle controls the symmetry of the whole system. For a Fermi wavelength comparable to the linear dimension of the CTS, the SOI-dependence of the conductance is sensitive to both the direction of bias and the rotation angle of the CTS. We propose a quantum ratchet which generates the directed current against AC bias with time-average zero by using spin-polarized electron injection. The relationship between the symmetry of the dot and the rectification effect is revealed, and is used as a mechanism for charge rectification.