High-resolution quasi-elastic neutron scattering spectroscopy was used to measure H2O and D2O hydrated RNA samples. The contribution of scattering from RNA was subtracted out by taking the difference of the signals between the two samples. The measurements were made at a series of temperatures from 270 K down to 180 K. The Relaxing-Cage Model was used to analyze the difference quasi-elastic spectra. We observed clear evidence of a fragile-to-strong dynamic crossover (FSC) at TL = 220 K in RNA hydration water. We further show that the mean-square displacement of the hydrogen atoms in both RNA and its hydration water exhibit a sharp change in slope at approximately the same temperature 220 K. This latter fact suggests that the dynamic transition (or the glass transition) in RNA is triggered by the abrupt change of mobility of the hydration water at its FSC temperature TL. ; Comment: 2 pages, 3 figures