Superconducting four-element patch array antenna was designed and fabricated using $high-T_{c}$ superconducting (HTS) thin film. The array antenna has single-feed circularly polarization and a resonance frequency of 11.85 GHz fur satellite communication system. To fabricate this antenna $YBa_2$$Cu_3$$O_{7-x}$(YBCO) superconducting thin films were deposited using rf-magnetron sputtering technique. Sequential rotation technique based on radiation elements($0^{circ}$ , $90^{circ}$, 1$80^{circ}$, $270^{circ}$ phase delay) was utilized to achieve circularly polarization. Simulated and measured results, the analysis on resonant frequency(fr), return loss, and bandwidth are presented. The results show that 10 dB return loss bandwidth of the array antenna is 11.04 GHz~12.59 GHz (13.15%) and 3dB axial ratio bandwidth is 11.42~12.52 GHz (9.2%).).).