Magnetic circular dichroism (MCD) is an optical probe of orbital time reversal symmetry breaking. Although frequency integrated MCD is related to the self-rotation contribution to orbital magnetization at zero field, its magnetic response generally differs from the thermodynamic orbital susceptibility. Here, we define the MCD susceptibility and derive general expressions for multiband systems using an electromagnetic U(1) gauge invariant approach. For insulators, the response contains contributions from the non-Abelian quantum metric, Berry curvature, and field induced interband mixing. For metals, a finite temperature Green function formulation separates the smooth response into Fermi sea and Fermi surface contributions. An independent Landau level calculation confirms the expressions for the zero-field MCD moment and its linear magnetic response. In a continuum model for twisted bilayer graphene, the MCD susceptibility vanishes within the charge neutrality gap, while the thermodynamic orbital susceptibility remains markedly diamagnetic. Near the gap edges, the orbital moment term dominates the response. Features near the van Hove energies are associated with density of states enhancement. These results clarify how the two susceptibilities reflect different orbital processes even for the same electronic structure and thus establish the MCD susceptibility as a distinct probe of orbital magnetic response.