A highly sensitive optical fiber torsion sensor with femtosecond laser-induced low birefringence SMF-based Sagnac interferometer (SI) is proposed and experimentally demonstrated in this paper. A straight-line waveguide positioned horizontally with respect to the fiber core is inscribed by the femtosecond laser in the cladding of the SMF, which leads to the asymmetry stress distribution in the SMF, and then gives rise to the low birefringence in the SMF. Compared with most of the previous reported SI based torsion sensors, there is no splicing joint in the femtosecond laser-induced low birefringence SMF-based SI, which lowers the transmission loss and makes the SI based torsion sensor more robust simultaneously. The experiment result shows that the proposed torsion sensor exhibits a torsion sensitivity of up to 3.2562 nm/degree, with the high torsion resolution of 0.003 degree. In contrast, the temperature cross-sensitivity and strain cross-sensitivity of the proposed torsion sensor are low, to -0.000055 degree/°C and 0.000013 degree/με, respectively, thus overcoming the cross-sensitivity problem resulting from temperature and strain. Moreover, theoretical analysis are carried out to compare with the experimental results to demonstrate the feasibility and good consistency.