The impact theory of Raman line broadening is applied to the broadening of the rotational Raman lines of diatomic molecules arising from electric multipole and anisotropic dispersion forces. Expressions are derived for the elastic and inelastic optical cross sections, and these are evaluated for the self-broadening in N2, O2, CO, and CO2, using values of the molecular constants obtained from sources independent of the line-broadening experiments. Included in the calculations are the "time", or "resonant", factors in the optical cross sections, and the resulting time integrals are explicitly evaluated for arbitrary multipole interactions, and anisotropic dispersion forces of second and fourth degree in the orientations. The overall agreement between the theoretical and experimental values of the magnitude of the half-widths is satisfactory, but a discrepancy appears in the variation of the broadening with the rotational quantum number. Possible explanations of this discrepancy are suggested in view of the results on foreign-gas broadening by monatomic gases.