Plasma screening effects on elastic electron–ion collision processes in a Lorentzian (kappa)-distribution plasma are investigated using the eikonal method. The electron–ion interaction potential is obtained by introducing a plasma dielectric function εκ. The semiclassical straight-line trajectory method is applied to the path of a projectile electron in order to investigate the variation of the eikonal phase as a function of impact parameter and spectral index κ. In the first-order eikonal approximation, the dynamic plasma screening effect on the eikonal phase is found to be a static screening effect, and depends only on the Debye length and spectral index. The position of the maximum of the differential elastic eikonal cross-section recedes from the ion core with increasing spectral index. The plasma screening effect on the eikonal cross-section increases with decreasing spectral index.