The anisotropic plasma screening effects on the eikonal scattering cross section for the electron–ion elastic collision are investigated in anisotropic plasmas in the presence of an externally applied magnetic field. The second-order eikonal analysis is employed to investigate the elastic collision process in magnetized plasmas. The classical straight line trajectory method is applied to the motion of the projectile electron in order to investigate the variation of the second-order eikonal phase as a function of the impact parameter and plasma parameters. The result shows that the major contribution of the magnetic field effect is found to be given by the second-order eikonal phase. It is also found that the eikonal scattering cross section including the anisotropic screening effect described by the effective interaction potential is always greater than that including the static screening effect obtained by the Debye–Hückel model. In addition, it is found that the eikonal cross section has the maximum value when the rotational energy with the Larmor frequency is equal to the thermal energy.