The Zeeman g-tensor parameterizes the interaction of an effective electronic spin with the homogeneous external magnetic field in the electron paramagnetic resonance (EPR) experiment. In this article, we describe a Kohn-Sham DFT (KS DFT)-based implementation of the g-tensor for periodic systems. Our implementation can be used, for example, for the first-principles calculation of a g-tensor of paramagnetic defects in solids. Our approach is based on the method of Van Lenthe et al.(20) in which the spin-orbital coupling is taken into account variationally. The method is implemented in the BAND program, a KS DFT implementation for periodic systems. The Bloch states are expanded in the basis of numerical and Slater-type atomic orbitals (NAOs/STOs). Our implementation does not rely on the frozen core approximation tacitly assumed in the pseudopotential schemes. The implementation is validated by calculating the g-tensor for small molecules as well as for paramagnetic defects in solids. In particular, we consider ozonide and hydrogen cyanide anion radicals in a KCl host crystal lattice.