  We model the effect of photon and ultra-light pseudoscalar mixing on the
propagation of electromagnetic radiation through the extragalactic medium. The
medium is modelled as a large number of magnetic domains, uncorrelated with one
another. We obtain an analytic expression for the different Stokes parameters
in the limit of small mixing angle. The different Stokes parameters are found
to increase linearly with the number of domains. We also verify this result by
direct numerical simulations. We use this formalism to estimate the effect of
pseudoscalar-photon mixing on the Cosmic Microwave Background (CMB)
polarization. We impose limits on the model parameters by the CMB observations.
We find that the currently allowed parameter range admits a CMB circular
polarization up to order $10^{-7}$.
