A relativistic energy density functional is constructed to investigate the Dirac effects on different properties of the structure and scattering of finite nuclei. The kinetic energy density has been derived within a relativistic extended Thomas-Fermi model and includes gradient corrections to second order in [h bar]. The effective mass and the volume term of the potential energy density have been obtained from a local density approximation to Dirac-Brueckner calculations of nuclear matter carried out with a realistic nucleon-nucleon interaction. This volume term is supplemented by the Coulomb energy and by conventional phenomenological surface and symmetry terms, and the few free parameters of the functional are suitably adjusted. Attention is then focused on the calculation of fission barriers of rotating nuclei and of the complex optical potential for heavy ion collisions at intermediate energies. It turns out that the effects of the density-dependent Dirac spinor which have been incorporated in this approach allow for a reasonable description of the investigated properties.