We present a general response function formalism describing the contribution of orientational dynamics of molecules at interfaces to spectroscopic line shapes in vibrational sum frequency generation (SFG). When reorientation occurs on the time scale comparable to vibrational dephasing, its dynamics can be extracted from polarization-selected SFG spectral line shapes. Unique features of orientational motion at interfaces are (1) the anisotropic case-specific equilibrium orientational distribution and (2) possible dynamic anisotropy (e.g., different in-plane versus out-of-plane relaxation rates), both of which must be taken into account. Within the small-step rotational diffusion model, we present solutions for two cases, the weak-confinement model, applicable when the deviations from the isotropic case are not severe, and the wobbling-in-a-cone model, which considers a hard-wall orienting potential. SFG line shapes are calculated for a rod-like chromophore as a function of the rotational diffusion rate. For certain equilibrium orientational distributions, orientational dynamics may result in anomalous bi-Lorentzian line shapes (two Lorentzians of different widths centered and the same frequency).