  We present polarisation data for 180 extragalactic sources extracted from the Australia Telescope 20 GHz (AT20G) survey catalog, and observed with the Australia Telescope Compact Array during a dedicated, high sensitivity run. For the sake of completeness we extracted the polarisation information for 7 extended sources from the 9-yr WMAP coadded maps at 23 GHz. The full sample of 187 sources constitutes a 99% complete sample of extragalactic sources brighter than S(20 GHz)=500mJy at the selection epoch with declination <-30 deg. The sample has a 91.4% detection rate in polarisation at 20GHz (94% if considering the sub-sample of point like sources). We have measurements also at 4.8 and 8.6 GHz within 1 month of the 20GHz observations for 172 sources to reconstruct the spectral properties of the sample in total intensity and in polarisation: 143 of them have a polarisation detection at all three frequencies. We find that there is no statistically significant evidence of a relationship either between the fraction of polarisation and frequency or between the fraction of polarisation and the total intensity flux density. This indicates that Faraday depolarisation is not very important above 4.8 GHz and that the magnetic field is not substantially more ordered in the regions dominating the emission at higher frequencies (up to 20 GHz). We estimate the distribution of the polarisation fraction and the polarised flux density source counts at 20GHz. 
A Polarisation Survey of Bright Extragalactic AT20G Sources