  We have calculated the optical conductivity of a disorder-free single
graphene sheet in the presence of spin-orbit coupling, using the Kubo
formalism. Both intrinsic and structural-inversion-asymmetry induced types of
spin splitting are considered within a low-energy continuum theory. Analytical
results are obtained that allow us to identify distinct features arising from
spin-orbit couplings. We point out how optical-conductivity measurements could
offer a way to determine the strengths of spin splitting due to various origins
in graphene.
