This work presents a four-port in-band full-duplex (IBFD) antenna that allows transmitting and receiving two sets of orthogonal co-circularly polarized signals, facilitating IBFD system applications. The single-element antenna is constructed using a six-port isolation network (SPIN) without the need for circulators, helping to reduce cost and facilitate integration. The transmit-receive isolation is accomplished via the isolation of power dividers and the cancellation guided by the coupling path of SPIN. The microwave network analysis method perfectly analyzes the operating mechanism of isolation and orthogonal co-circular polarization. The measured results confirm that this design achieves excellent two sets of orthogonal co-circular polarization. The measured results show that the 10-dB impedance bandwidth is 24.2%, the 3-dB axial-ratio bandwidth is 23.5%, and the measured 30-dB isolation bandwidth is 3.52-4.15 GHz (16.4%) with a maximum isolation of 53.2 dB.