We present a novel scheme to calculate electronic g-tensor values of doublet-state systems within a density functional method and discuss the implementation and results of first applications. The method employs two-component eigenfunctions of the Kohn-Sham equation where spin-orbit effects are taken into account self-consistently. Therefore, the g-tensor can be treated as first-order property with respect to the perturbation by external magnetic field alone. The Zeeman energy splitting, an inherently relativistic effect, is naturally and transparently determined by the two-component ground-state wave function (Kramers doublet) without invoking virtual states. Abandoning the widely accepted perturbative treatment of the spin-orbit term makes the present method also applicable to molecular systems with considerable spin-orbit interaction. Conceivable improvements of the method performance are proposed and discussed.