Stimulated Raman amplification is observed for the first time in the silicon core fiber (SCF) platform. The SCFs were tapered to obtain sub-micrometer core dimensions and low optical transmission losses, facilitating efficient spontaneous scattering and stimulated Raman amplification using a continuous-wave pump source with milliwatt power levels. A maximum on-off gain of 1.1 dB was recorded at a pump power of only 48 mW with our numerical simulations, indicating that gains up to 6dB are achievable by increasing the fiber length. This work shows that the SCF platform could open a route to producing compact and robust all-fiber integrated Raman amplifiers and lasers across a broad wavelength region.