We present a theoretical and numerical study of coherent anti-Stokes Raman scattering Fourier ptychography microscopy (CARS-FPM), a scheme that has not been considered so far in the previously reported CARS wide-field imaging schemes. In this approach, the distribution of the Raman scatterer density of the sample is reconstructed numerically from CARS images obtained under various angles of incidences of the pump or Stokes beam. Our inversion procedure is based on an accurate vectorial model linking the CARS image to the sample and yields both the real and imaginary parts of the susceptibility, the latter giving access to the Raman information, with an improved resolution.