We report on a polymer-based porous-core photonic crystal fiber for simultaneous high-birefringent and low-loss propagation of narrowband terahertz (THz) electromagnetic waves. The high birefringence is induced by using rotated elliptical air holes inside the porous-core. The fiber is numerically analyzed with an efficient finite-element method. The simulation results exhibit an extremely high birefringence of and a very low effective material loss of at an operating frequency of 1 THz. Moreover, we have found an optimal ( is an odd integer). Other modal features of the fiber, such as confinement loss, power fraction, effective area, bending loss, and dispersion, also have been analyzed. We anticipate that the proposed fiber would be suitable in polarization maintaining THz wave guidance applications.