We propose and investigate a compact optical fiber sensor that aims to measure the torsion in both amount and direction with high sensitivity. This sensor is configured by a triangular-prism-shaped long-period fiber grating, which is fabricated by the high frequency CO2 laser polished method. The unique design of the triangular-shaped structure breaks the rotational symmetry of the optical fiber and provides high sensitivity for torsion measurement. In preliminary experiments, the torsion response of the sensor achieves a good stability and linearity. The torsion sensitivity is 0.54 nm/(rad/m), which renders the proposed structure a highly sensitive torsion sensor.