In low earth orbiting satellite communication systems, antennas are key elements for radio frequency transmitters and receivers. There are different types of antennas used on satellite communication systems. One of them is the antenna used in payload data transfer communication subsystem. Payload data transmitters for space segment should utilize the radio frequency power efficiently due to the limited power budget of the spacecraft. For low elevation angles of a low earth orbiting satellite, the free space loss increases as expected and it should be compensated. One way of this compensation is to employ an antenna having isoflux pattern. Therefore, in this paper, a circularly polarized X-Band choked ring horn antenna is designed, optimized and manufactured due to its isoflux radiation characteristic and medium power handling capability. Initially, an analytical approach from the literature is explained and then the physical dimensions of the proposed antenna are optimized, iteratively, employing a commercially available electromagnetic solver. Next, a prototype has been manufactured to verify the radiation, return loss and port isolation characteristics and they are presented in the related section. Moreover, the results of the presented antenna have been compared to the ones available in the literature. These comparisons show that gain of the designed antenna at +/- 64 degrees elevation angle has higher gain with respect to the compared ones. In addition, its axial ratio value is smaller than 6.5 dB for different azimuth angles between 8025 and 8400 MHz. Unlike the other studies given in the literature that have gain higher than 2 dB at +/- 64 degrees elevation angle, in this study all design parameters have been presented to utilize through the operating bandwidth.