We investigate the possibility of implementing coherent anti-Stokes Raman spectroscopy (CARS) with a single laser beam passed through a one-dimensional scattering object. The effect of the random scattering is emulated by shaping the laser pulses with a spectral mask corresponding to the transmission spectrum of a random layered medium. Raman resonances are retrieved through correlation analysis of the CARS spectrum. We study the effect of the scattering parameters on the resolution of the method, and show that improvement of the spectroscopic sensitivity can be achieved by compensating the phase distortions introduced by the scatterer.