Ion mobility spectrometry (IMS) assumes increasing prominence among the tools for characterization of gas-phase ions and analysis of complex mixtures. The assignment of features observed in IMS experiments to specific structures necessitates the calculation of mobilities for plausible candidate geometries. All previous methods for these calculations have assumed that the ion-buffer gas collisions are fully elastic and that the drifting ions cannot rotate during a collisional event. This paradigm does not mesh well with the fact that the measured quantity is the orientationally averaged collision integral. Here we model the effect of the thermal rotation of drifting ions on their mobility. Simulations show that the cross sections for rotating objects are greater than those for static ones because a molecular image "blurs out" over the duration of collision. This increase is particularly significant for light and elongated ions. For a given ion, the effect is dramatically larger in heavy buffer gases, in some cases exceeding 20%. Present findings reveal the importance of accounting for the nonelasticity of scattering in ion mobility calculations.