Limits on global cosmic birefringence using radio sources

We have made measurements of the difference between the position angle (PA) on the sky and the polarization position angle (PPA) of radio sources using data from a combination of the Radio Fundamental Catalogue (RFC) across a range of frequencies between 2.7 and 15~GHz and Cosmic Lens All Sky Survey (CLASS) which observes polarization at 8.4~GHz (X-band). For the 2111 sources with jet PAs measured in the X-band and a known redshift, the distribution is peaked at $\approx 0^{\circ}$ as expected for no birefringence and it can be modelled by two populations: one which is a Gaussian with mean $\mu_{\beta}=(0.2\pm 1.0)^{\circ}$ and standard deviation $\sigma_{\beta}=(14.7\pm 1.1)^{\circ}$ and the other a uniform distribution of sources which are a fraction $f_\beta=0.72\pm 0.02$ of the total. Uncertainties in $\mu_\beta$ can be reduced to $\approx 0.6^{\circ}$ by stacking measurements of the PA from other wavebands. We find that limits of $\approx 0.1^{\circ}$ might be possible with a sample of $\sim 10^5$ similarly selected sources and that this could provide a confirmation of recent claims of global birefringence made using the Cosmic Microwave Background observations from the {\it Planck} satellite.