Thinner substrate designs of square and circular microstrip antennas using fractal variations of U-shape and half U-shape slot cut ground plane are proposed for circularly polarized response. The 1st, 2nd, and 3rd order fractal variations of slots on the ground plane are studied. The fractal slot cut variations degenerate patch fundamental mode into dual orthogonal resonant modes, and an optimum spacing between them yields circularly polarized characteristics. Amongst all the designs, circular microstrip antenna using the 1st order fractal U-slot design yields the optimum result. It offers axial ratio bandwidth of 60 MHz (2.14%) with a broadside radiation pattern and peak gain of 5.5 dBi, on a substrate of 0.02λg thickness and patch area 1.44λg. Against the reported designs, the current work presents a low profile single patch circularly polarized configuration. © 2023, Electromagnetics Academy. All rights reserved.