As an important emitter for terahertz radiation, photoconductive antenna arrays are limited in their application flexibility due to the fixed polarization state of traditional antennas. In response to this issue, we have designed and studied a polarization-adjustable four-element terahertz gallium arsenide photoconductive antenna array, aiming to enhance its versatility and applicability in various applications. By precisely controlling the excitation of each element, the antenna array can achieve precise control of linearly and circularly polarized terahertz waves through in-phase unequal amplitude excitation and phase difference excitation. The results show that with in-phase unequal amplitude excitation, flexible control of linearly polarized terahertz waves within a 360-degree range can be achieved. With a 90-degree phase difference excitation, circularly polarized terahertz waves are generated, with a -10 dB impedance bandwidth range of 0.057 THz to 1.013 THz and a relative bandwidth of 178.69%. The axial ratio bandwidth range is 0.815 THz to 0.947 THz, with a relative bandwidth of 14.98%.