This table contains polarization data for 180 extragalactic sources extracted from the Australia Telescope 20-GHz (AT20G) survey catalog and observed with the Australia Telescope Compact Array (ATCA) during a dedicated, high sensitivity run (sigma_P ~ 1 mJy). For the sake of completeness, the authors extracted the polarization information for seven extended sources from the 9-yr Wilkinson Microwave Anisotropy Probe co-added maps at 23 GHz. The full sample of 187 sources constitutes a ~ 99% complete sample of extragalactic sources brighter than S_20GHz = 500 mJy at the selection epoch with Declination below -30^o. The sample has a 91.4% detection rate in polarization at ~ 20 GHz (94% if considering the sub-sample of point-like sources). The authors have measurements also at 4.8 and 8.6 GHz within ~1 month of the 20-GHz observations for 172 sources so as to reconstruct the spectral properties of the sample in total intensity and in polarization: 143 of them have a polarization detection at all three frequencies. The authors find that there is no statistically significant evidence of a relationship either between the fraction of polarization and frequency or between the fraction of polarization and the total intensity flux density. This indicates that Faraday depolarization 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). The authors estimate the distribution of the polarization fraction and the polarized flux density source counts at ~20 GHz. The selection of the sample was based on the list of confirmed AT20G sources available at the epoch of these observations (2006 October). The authors selected all objects with flux density S_20GHz > 500 mJy and Declination below -30^o, excluding the Galactic plane region (|b| <= 1.5o^) and the Large Magellanic Cloud (LMC) region (inside a circle of 5.5^o radius centered at RA =05:23:34.7 and Dec=-69:45:22 in J2000.0 coordinates). This resulted in a complete sample of 189 sources. The observations were taken on October 1, 2006 using the most compact hybrid configuration of ATCA, H75, excluding the data from the farthest antenna. The longest baseline of this configuration is 75 m, and its T-shape ensures adequate Fourier coverage for snapshots taken on a relatively small range of hour angles and at high elevation. In a number of cases, indicated by source_flags values of 's', 'f' or 'w', the highest frequency data is not at 18 GHz, but at 20 or 23 GHz. This table was created by the HEASARC in January 2015 based on the CDS Catalog J/MNRAS/436/2915 file table2.dat. This is a service provided by NASA HEASARC .