We consider the problem of designing a circularly polarized Fabry-P'erot cavity (FPC) antenna for S-band sensing applications such as satellite navigation and communication. The spatial distribution of peripheral roughness of the unit cell of FPC's partially reflecting surface (PRS) serves as an important design optimization criterion. However, the evaluation of each candidate design using a full-wave solver is computationally expensive. To this end, we propose a deep generative adversarial network (GAN) for realizing a surrogate model that is trained with input-output pairs of antenna designs and their corresponding patterns. Using the GAN framework, we quickly evaluate the characteristics of a large volume of candidate designs and choose the antenna design with an axial ratio of 0.4 dB, a gain of 7.5 dB, and a bandwidth of 269 MHz.