The effect of the relativistic spin-orbit (SO)interaction on the bonding in the early actinides has been investigated by means of electronic-structure calculations. Specifically, the equation of state (EOS) for the face-centered cubic (fcc) model systems of these metals has been calculated from the first-principles density-functional (DFT) theory. Traditionally, the SO interaction in electronic-structure methods is implemented as a perturbation to the Hamiltonian that is solved for basis functions that explicitly do not depend on SO coupling. Here this approximation is shown to compare well with the fully relativistic Dirac treatment. It is further shown that SO coupling has a gradually increasing effect on the EOS as one proceeds through the actinides and the effect is diminished as density increases.