Due to its unique electromechanical properties, nanomaterial has become a promising material for the sensing elements of strain sensors. Tensile strain is the most well-studied deformation. Torsion is another deformation happening in daily life but has not been well understood. In the present work, a torsion sensor was prepared by wrapping graphene woven fabrics (GWFs) around a polymer rod at a fixed winding angle. The GWFs sensor showed an ultra-high sensitivity with a detection limit as low as 0.3 rad/m, indicating its potential application in highly precise measurement of low torsions. The GWFs could pre-strained before wrapped on the PDMS mode to improve tolerance of the sensor to high torsion. The microstructure of the GWFs under different torsion levels was monitored using an optical microscope. The results demonstrate the formation of GWFs waves and cracks under high torsion, which is critical to the electromechanical properties of GWFs sensor.