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The propagation of Riemann-Silberstein (RS) vortices for Gaussian vortex beams with topological charges m=+1 through a lens is studied. It is shown that if there is an ideal lens, a RS vortex and a circular edge dislocation appear for Gaussian on-axis vortex beams, while only RS vortices take place for Gaussian off-axis vortex beams. In the presence of an astigmatic lens, there exist RS vortices but no edge dislocations for both Gaussian on-axis and off-axis beams. By varying the astigmatic coefficient, the off-axis parameter, and the propagation distance, the motion, creation, and annihilation of vortices may take place, and in the process, the total topological charge of RS vortices remains unchanged.