We demonstrate the fabrication of an angle-chirped long-period fiber grating (ACLPFG) in a single-mode fiber via CO2 laser pulses. Because of the Berry phase introduced by the ACLPFG, the interference acquires an extra phase difference determined by the torsion of the device. By using that unique characteristic of the proposed device, a high sensitivity sine function torsion response is achieved. The torsion sensitivity is significantly improved, and the temperature crosstalk is effectively avoided by using the relative measurement technology. The torsion sensitivity is ~16 folds (~0.94 nm/ (rad/m)) higher than that of the normal long-period fiber grating (LPFG) with only ~0.006 nm/°C temperature crosstalk within the range of 25-80 °C, which is ~10 folds lower than that of the normal LPFG.