We present the design of a high birefringence hollow core with nested anti-resonance nodeless fiber (HC-NANF). This model is designed for terahertz guidance made by TOPAS copolymer. The finite element method is used to study the properties of the proposed fiber: effective material loss, confinement loss, and birefringence. In this model, the cladding consists of four circular anti-resonant tubes: two tubes aligning in the horizontal axis and two tubes aligning in the vertical axis. Each circular anti-resonant tube consists of two circular nested tubes. First, we optimize the thickness of circular nested tubes due to anti-resonance reflecting guidance mechanism to achieve the lowest loss. The simulation results show that the thickness of 0.09 mm is suitable for operating at 1 THz. To achieve the birefringence, we attempted to rotate the inner circular nested tube with two patterns: symmetric and asymmetric rotations. The simulation results show that only the asymmetric rotation can provide the birefringence in the structure. It also shows that the birefringence can be adjusted by rotating the inner circular nested tube with respect to the core radius. Finally, the orthogonal birefringence of the proposed design from HC-NANF is found to be higher than 10-4. This study offers an alternative model to provide the birefringence in THz regime, which might be relevant for future polarization related applications.