  We consider the magnetic circular dichroism spectrum of a crystal with broken
time-reversal symmetry in the electric-dipole approximation. Using the
Kubo-Greenwood formula for the absorptive part of the antisymmetric optical
conductivity, its frequency integral is recast as a ground-state property. We
show that in insulators this quantity is proportional to the circulation of the
occupied Wannier orbitals around their centers (more precisely, to the
gauge-invariant part thereof). This differs from the net circulation, or ground
state orbital magnetization, which has two additional contributions: (i) the
remaining Wannier self-rotation, and (ii) the ``itinerant'' circulation arising
from the center-of-mass motion of the Wannier orbitals, both on the surface and
in the interior of the sample. Contributions (i) and (ii) are not separately
meaningful, since their individual values depend on the particular choice of
Wannier functions. Their sum is however gauge-invariant, and can be inferred
from a combination of two experiments: a measurement of the magneto-optical
spectrum over a sufficiently wide range to evaluate the sum rule, and a
gyromagnetic determination of the total orbital magnetization.
