  Standard cosmological models do predict a measurable amount of anisotropies
in the intensity and linear polarization of the Cosmic Microwave Background
radiation (CMB) via Thomson scattering, even though these theoretical models do
not predict circular polarization for CMB radiation. In other hand, the
circular polarization of CMB has not been excluded in observational evidences.
Here we estimate the circular polarization power spectrum $C_{l}^{V(S)}$ in CMB
radiation due to Compton scattering and non-linear photon-photon forward
scattering via Euler-Heisenberg Effective Lagrangian. We have estimated the
average value of circular power spectrum is $1(l+1)\,C_{l}^{V(S)}/(2\pi)\sim
10^{-4}\mu\,K^2$ for $l\sim300$ at present time which is smaller than recently
reported data (SPIDER collaboration) but in the range of the future achievable
experimental data. We also show that the generation of B-mode polarization for
CMB photons in the presence of the primordial scalar perturbation via
Euler-Heisenberg interaction is possible however this contribution for B-mode
polarization is not remarkable.
