We report on an accurate measurement of the frequency splitting of an optical rotating ring microcavity made out of calcium fluoride. By measuring the frequencies of the clockwise and counter-clockwise coherent Raman emissions confined in the cavity modes, we show that the frequency splitting is inversely proportional to the refractive index of the cavity host material. The measurement has an accuracy of 1% and unambiguously confirms the classical theoretical prediction based on special theory of relativity. This Letter also demonstrates the usefulness of the ring Raman microlaser for rotation measurements.