  We construct a minimal theory describing the optical activity of a thin sheet
of a twisted material, the simplest example of which is twisted bilayer
graphene. We introduce the notion of "twisted electrical conductivity", which
parametrizes the parity-odd response of a thin film to a perpendicularly
falling electromagnetic waves with wavelength larger than the thickness of the
sheet. We show that the low-frequency Faraday rotation angle has different
behaviors in different phases. For an insulator, the Faraday angle behaves as
$\omega^2$ at low frequencies, with the coefficient being determined by the
linear relationship between a component of the electric quadrupole moment and
the external electric field. For superconductors, the Faraday rotation angle is
constant when the frequency of the incoming EM waves is below the
superconducting gap and is determined by the coefficient of the Lifshitz
invariant in the Ginzburg-Landau functional describing the superconducting
state. In the metallic state, we show that the twisted conductivity is
proportional to the "magnetic helicity" (scalar product of the velocity and the
magnetic moment) of the quasiparticle, averaged around the Fermi surface. The
theory is general and is applicable to strongly correlated phases.
