A strong Raman enhancement to the four-wave mixing (FWM) conversion efficiency is obtained in a silicon core fiber (SCF) when pumped with a continuous-wave (CW) source in the telecom band. By tapering the SCFs to alter the core diameter and length, the role of phase-matching on the conversion enhancement is investigated, with a maximum Raman enhancement of ∼15 dB obtained for an SCF with a zero dispersion wavelength close to the pump. Simulations show that by optimizing the tapered waist diameter to overlap the FWM phase-matching with the peak Raman gain, it is possible to obtain large Raman enhanced FWM conversion efficiencies of up to ∼2 dB using modest CW pump powers over wavelengths covering the extended telecom bands.