The tyrosyl radical in galactose oxidase is covalently cross-linked to a neighboring cysteine residue through a thioether bond. The role of this sulfur cross-link has been discussed ever since the crystal structure of the enzyme was solved. In the present work, the ab initio multiconfigurational linear response method is applied to calculate the g-tensor of unsubstituted and thioether substituted phenoxyl radicals. In contrast to some previous interpretations, but in agreement with recent EPR measurements, we find that the sulfur substitution induces only minor shifts in the g-tensor components. The spin distribution retains the odd-alternant pattern of the unsubstituted radical and only a small amount of spin is localized to the sulfur center.