The effect of local rigid rotations of the LiNbO$_3$ structure on the optical response has been theoretically explored and compared to experimental data obtained after irradiation with F (20–22 MeV), O (20 MeV) and Mg (39 MeV) ions. The calculations account for the main trends of the ordinary and extraordinary refractive indices measured after the initial stage of irradiation, namely, decrease in birrefringence and approximate invariance of the average refractive index. Moreover, experimental data are quantitatively consistent with a distribution function $\exp [-\theta/\theta_0]$ for the rotation angle with respect to the trigonal (Z-axis) and isotropic azimuthal angle $ϕ$. The corresponding $\theta_0$ angle is in the range 4.6–7.0$^∘$ depending on ion and energy (stopping power). The model also predicts a significant reduction in second-harmonic generation (SHG) yield with fluence, comparable although somewhat lower than found by experiment.