The photoconductive antenna array is a crucial emitter of terahertz radiation, with its polarization characteristics playing a significant role in beam control, imaging resolution, and signal transmission efficiency. However, current research predominantly focuses on antenna designs with fixed polarization states, lacking comprehensive studies on adjustable polarization performance. This limitation reduces their flexibility and applicability in practical applications. In this paper, we design and investigate a polarization-adjustable four-element terahertz gallium arsenide photoconductive antenna array. Our goal is to achieve precise control of linearly and circularly polarized terahertz waves by manipulating the excitation mode of the array elements. The results demonstrate that using in-phase unequal amplitude excitation allows for flexible control of linearly polarized terahertz waves within a 360° range by adjusting the excitation amplitude of each element. Under 90° phase-difference excitation, circularly polarized terahertz waves are achieved, with a -10 dB impedance bandwidth of 0.057 THz to 1.013 THz, a relative bandwidth of 178.69%, and a center frequency of 0.535 THz. The axial ratio bandwidth is 0.815 THz to 0.947 THz, with a relative bandwidth of 14.98% and a center frequency of 0.881 THz. In traditional photoconductive antenna arrays, the combination of the excitation amplitude, phase of each element, and the influence of the pump laser often results in the emitted terahertz waves being predominantly elliptically polarized. Our approach overcomes these limitations, providing a more versatile and efficient solution for terahertz wave emission and control.