  We present a general formula of the orbital magnetization of disordered
systems based on the Keldysh Green's function theory in the gauge-covariant
Wigner space. In our approach, the gauge invariance of physical quantities is
ensured from the very beginning, and the vertex corrections are easily
included. Our formula applies not only for insulators but also for metallic
systems where the quasiparicle behavior is usually strongly modified by the
disorder scattering. In the absence of disorders, our formula recovers the
previous results obtained from the semiclassical theory and the perturbation
theory. As an application, we calculate the orbital magnetization of a weakly
disordered two-dimensional electron gas with Rashba spin-orbit coupling. We
find that for the short range disorder scattering, its major effect is to the
shifting of the distribution of orbital magnetization corresponding to the
quasiparticle energy renormalization.
