A method has been developed for the calculation of the g-tensor of Kramers doubler open shell molecules, which uses the spinor of the unpaired electron of the paramagnetic molecule, obtained from a density functional calculation. Spin-orbit coupling is taken into account variationally using the zeroth-order regular approximation (ZORA) to the Dirac equation. The problem of gauge dependence is solved by using gauge including atomic orbitals (GIAO’s), The method gives fair agreement with experimental values for the g values of some small test molecules NO2, HCO, and TiF3.