The polarized Raman spectra of a natural air hydrate single crystal from a deep ice core recovered at Dye-3 Greenland have been measured in order to examine the crystal-orientation dependence of the Raman spectra. Since the crystal had facets, the orientation of the crystal was determined by using the Miller indices of facets. When the angle theta between the polarization plane of the incident laser beam and the direction of [111] of the crystal varied, it was observed that the intensities of the stretching modes of the two major guest molecules (nitrogen and oxygen) varied with theta. Since the dodecahedron cage in the air hydrate are distorted along the [111] axis, the variations of the scattering intensities of N-2 and O-2 have been calculated by using a simple model that assumes N-2 and O-2 are on the plane of {111} in the dodecahedron cage, The results obtained from experiments are consistent with the calculations made by using this simple model. We concluded that the anisotropy of the intensities of N-2 and O-2 was caused by the anisotropic rotation of the guest molecules in the distorted dodecahedron cage.