Time-correlated Stokes-anti-Stokes (SaS) scattering has been studied in different transparent media, more frequently in diamond. While the nonclassical nature of the SaS scattered photons has been well established, the presence of entanglement in this spontaneous four-wave mixing process has not been demonstrated. Here, we show the violation of the Bell-type Clauser-Horne-Shimony-Holt inequality for the polarization of SaS photon pairs near a Raman resonance in diamond. The degree of entanglement depends on the detuning of the photon pairs from the degenerate two-photon pump and on the orientation of the polarization of the incident light with respect to the crystallographic orientation of the sample. This result opens up the possibility to tailor the quantum state of photon pairs without stringent constraints of phase matching and to combine quantum optics and SaS Raman spectroscopy for new applications in materials science and quantum information.