In this paper, a comprehensive passive torsion measurement is performed firstly in a 40-cm-long polarization maintaining fiber-based Sagnac interferometer (PMF-SI), and the non-linear torsion response is found and investigated. Then, a fiber laser torsion sensor (FLTS) with a dual-ring-cavity structure is proposed and experimentally demonstrated, in which the PMF-SI is utilized as the optical filter as well as the sensing unit. In particular, the highly sensitive linear range is adjusted through fine phase modulation, and owing to the flat-top feature of fringes, an ~83.6% sensitivity difference is effectively compressed by the generated lasing. The experimental results show that, without any pre-twisting, the ultra-wide linear response from –175 to 175 rad/m is gained, and the torsion sensitivities are 2.46 and 1.55 nm/rad with high linearity (>0.99) in the clockwise and anti-clockwise directions, respectively. Additionally, a high extinction ratio (>42 dB) and small line-width (~0.14 nm) are obtained in the proposed FLTS, and the corresponding detection limit reaches 0.015 rad/m.