We investigate the astigmatic transformation of vortex and nonvortex cylindrical vector beams (CVBs) of different orders performed by a cylindrical lens. The total intensity does not change when the cylindrical lens rotates; however, the individual components can be significantly transformed. We show that the modulus of the polarization order |p| of the investigated CVBs can be defined by the astigmatic intensity distribution. In addition, in the case of vortex CVBs, it is only possible to determine a change in the sign of the order of the optical vortex. The experimentally obtained results are in agreement with the modeling results. The results obtained can be useful in optical communications for the detection of vortex beams with different polarization states and in polarization-dependent laser nanopatterning of various materials.