The optical performance characteristics of anti‐resonant hollow‐core fibers (known as AR‐HCFs or ARFs) are improving rapidly, but the polarization maintaining issue with these fibers remains unresolved. Although a regular nonbirefringent ARF can maintain high polarization purity under static conditions, it cannot resist mechanical disturbances. In this work, by designing a bi‐thickness semi‐tube ARF structure with fourfold rotational symmetry, the first ARF with a level of birefringence close to 10−4 is fabricated. The proposed ARF features a combination of phase birefringence of 9.1 × 10−5, a minimum loss of 185 dB km−1, a bandwidth of 133 nm, and single‐mode operation. Furthermore, the ARF shows high resistance to fiber bending and wide‐range temperature variations, thus confirming that this carefully designed ARF can serve as a practical workhorse in polarization‐related optical fiber applications.