The realization of cross-polarization conversion has attracted great interest in polarization conversion metasurfaces (PCMs), particularly due to polarization manipulation of electromagnetic (EM) waves with small size and low loss. An azimuth-rotation-independent (ARI) cross-polarization converter is a kind of 90° polarization rotator, which can rotate the polarization of linearly polarized incident electromagnetic (EM) waves with an arbitrary polarization direction to the orthogonally polarized transmitted EM waves. In this paper, we study the symmetry properties of chiral metasurfaces using the Jones matrix method for ARI 90° polarization rotators. The previous designs could only address C4 symmetry, but with this approach, the derived unit cell structure of the ARI PCM should possess Cn(n ≥ 3, n ∈ N+) symmetry. To confirm the design concept, two chiral structures with different symmetries are investigated by full-wave numerical simulations. The experimental results are also carried out and excellently agree with the simulated results. It could be used for polarization conversion applications and further utilized in antenna applications, polarization detection, and telecommunication applications.