The Jones matrix method analysis of Raman induced Kerr effect spectroscopy (RIKES) is presented. The intensity of weak linear polarized monochromatic probe beam is not only dependent on the Jones matrix of each optical device in pump- probe technique, but also dependent on the Jones matrix of nonlinear medium sample, in which an intensity dependent dichromism and birefringence are induced by a strong circularly polarized pump beam. Take account of the disadvantage factors of the additional static birefringe in the sample and other optics, which will produce a background intensity in the polarized signal. The complete expression of power transfer function and the annihilation condition of RIKES are derived. The PIKES experimental results of the toluene (C7H8) are given briefly.