Spiral polarization rotators, rotating polarization ellipse axes clockwise or counterclockwise, depending on the azimuth angle in the transverse plane, are considered. It is shown that spiral polarization rotators lead to a change in the order of optical vortices with circular polarization. A comparative analysis of spiral rotators of two types (polar and non-polar) is carried out, using a mirror that allows light to pass in the opposite direction through the rotator. The effect of spiral rotators on optical vortices in a resonator is studied. It is shown that spiral rotators can preserve or accumulate changes of the vortex order during the passage of the beam in both directions. The properties of the spiral rotator and the cube-corner reflector with a special phase-correcting coating, as a diffractive polarization-optical element, are compared.