Nonspherical large cages in structure I (sI) clathrates impose non-uniform motion of nonspherical guest molecules and anisotropic lineshapes in NMR spectra of the guest. In this work, we calculate the lineshape anisotropy of the linear CO2 molecule in large sI clathrate cages based on molecular dynamics simulations of this inclusion compound. The methodology is general and does not depend on the temperature and type of inclusion compound or guest species studied. The nonspherical shape of the sI clathrate hydrate large cages leads to preferential alignment of linear CO2 molecules in directions parallel to the two hexagonal faces of the cages. The angular distribution of the CO2 guests in terms of a polar angle θ and azimuth angle  and small amplitude vibrational motions in the large cage are characterized by molecular dynamics simulations at different temperatures in the stability range of the CO2 sI clathrate. These distributions are used to calculate the NMR powder spectrum of CO2 at different temperatures. The experimental 13C NMR lineshapes of CO2 guests in the large cages show a reversal of the skew between the low temperature (77 K) and the high temperature (238 K) limits of the stability of the clathrate. Good agreement between experimental lineshapes and calculated lineshapes is obtained. No assumptions regarding the nature of the guest motions in the cages are required.