The perturbation approach is presented here for the first time for the analysis of an inhomogeneous circularly polarized rectangular dielectric resonator (DR) antenna (DRA). The inhomogeneous permittivity is created by perturbing a rectangle-shaped region of different material inside the rectangular dielectric resonator antenna (RDRA). The orthogonal degenerate modes with a phase difference of TE111x, and TE111y, are excited simultaneously for achieving circular polarization. A simple expression for the calculation of the resonant frequency and optimal axial ratio point for a circularly polarized (CP) inhomogeneous RDRA is presented here. Theoretical results obtained from the proposed theory are compared with theoretical, simulated, and experimental data available in the literature. The proposed analysis results show optimal axial ratio point calculations within a 1% range of the simulated and experimental data, which is better than the previous transverse transmission line reported method, having an error of approximately 4%. The advantages, accuracy, and simplicity of perturbation theory for DR are discussed in detail. The proposed theory can be easily extended for higher order modes and other shapes of material perturbation and anisotropic DRAs. The proposed technique will help in incorporation of the perturbation in the DR so that CP radiation can be obtained in an easy way.