Measurement of magnetic circular dichroism (MCD) anisotropy has contributed greatly to the understanding of the electronic structure of transition metal ion centers in both biological and nonbiological materials. Compared to previous methods, optically detected electron paramagnetic resonance experiments can measure MCD anisotropy with dramatically improved orientational resolution. In this paper the relevant theory for systems with an isolated Kramers doublet ground level is derived and its application illustrated using a transition metal ion center in a protein: low spin ferric haem.