In this work, we conduct a comprehensive computational study using the finite element method for the design of a terahertz (THz) polarization converter based on a low-absorption polymer. The dimensions of the polymer THz wave plate studied in this work were chosen considering the capacity to provide a broadband phase difference. Our numerical simulations show that for the elliptical and catenary pillar structures, we observe that the amplitude of the transmission spectra for the x-polarization component is 10 times lower than the y-polarization component. However, the phase difference spectra of the elliptical structure show a conversion of linear polarization into quasi-circular over a range of 0.6 THz, while for the catenary structure, a change from linear polarization into quasi-elliptical between 0.4 and 1.2 THz.