  It is known that the dominant contribution of primordial anisotropies of
Cosmic Microwave Background (CMB) is linearly polarized via Compton scattering.
However circular polarization of this anisotropy has not been observed up to
now, but it has not been excluded in observational evidence. Here we show that
the Euler-Heisenberg Effective Lagrangian can generate circular polarization in
CMB. This generation is calculated by using the Quantum Boltzmann Equation for
the time evolution of the Stokes parameter. Also, we estimate the Faraday
conversion phase in order of $10^{-13} $ due to this Lagrangian which gives a
lower bound on circular polarization of CMB.
