In this paper, we report a novel in-fiber Mach-Zehnder interferometer based directional torsion sensor, in which a section of two-mode fiber is sandwiched between two single mode fibers by over core-offset splicing technique. The variety of fringe visibility demonstrates the strong dependence on offset and fiber length. For the first time the near zero visibility at 0° rotating state is obtained by fine offset-modulation. The experimental results show that, with 0° turning point, the counter-clockwise to the clockwise direction can be recognized by the reversal from peak to dip of fringes. Moreover, a competitive sensitivity of 21.485 dB/(rad/cm) is gained with high linearity and low-temperature crosstalk in the range from -40 rad/m to 40 rad/m. Without any pre-twisting, our fiber torsion sensor is small size, ease of fabrication, cost efficiency and very potential in the applications of industrial and artificial intelligence.