The structure of twisted namatic liquid crystal does not change under weak magnetic field. The rotation of polarization of light in the twisted nematic liquid crystal with the applied weak magnetic field is analyzed using the dielectric rate tensor. The theoretical results show that linearly polarized light transmitting this liquid crystal can produce left-hand and right-hand elliptically polarized light, which corresponds to the different speed of propagation. This leads to the rotation of polarization of light when it passes through this liquid crystal. A method to calculate rotation angle which results from the combination of the left-hand and right-hand elliptically polarized light is given. The dependence of the transmitted ratio of light on the applied magnetic field is founded. Under the same wavelength of light, the more intense the magnetic field strength, the larger the rotated angle of polarization of light. At the same magnetic field strength, The shorter the wavelength of light, the larger the rotated angle of polarization of light. When the directors of liquid crystal are parallel to the direction of the magnetic field, the polarization rotation of light can also been observed.