We have carried out observations at 18.5 GHz with the Australia Telescope Compact Array (ATCA) of 250 out of the 258 Southern extragalactic sources in the complete 5 GHz 1 Jy sample by Kühr et al. (1981). In this paper we focus on the polarization properties of this sample, while other properties will be addressed in a future paper. In our analysis we subdivide the sample into flat and steep spectrum sources following Stickel et al. (1994) classification, where spectral indices were measured bet...