We present polarization measurements of extragalactic radio sources observed during the Cosmic Microwave Background polarization survey of the Q/U Imaging Experiment (QUIET), operating at 43 GHz (Q-band) and 95 GHz (W-band). We examine sources selected at 20 GHz from the public, $>$40 mJy catalog of the Australia Telescope (AT20G) survey. There are $sim$480 such sources within QUIETs four low-foreground survey patches, including the nearby radio galaxies Centaurus A and Pictor A. The median error on our polarized flux density measurements is 30--40 mJy per Stokes parameter. At S/N $> 3$ significance, we detect linear polarization for seven sources in Q-band and six in W-band; only $1.3 pm 1.1$ detections per frequency band are expected by chance. For sources without a detection of polarized emission, we find that half of the sources have polarization amplitudes below 90 mJy (Q-band) and 106 mJy (W-band), at 95% confidence. Finally, we compare our polarization measurements to intensity and polarization measurements of the same sources from the literature. For the four sources with WMAP and Planck intensity measurements $>1$ Jy, the polarization fraction are above 1% in both QUIET bands. At high significance, we compute polarization fractions as much as 10--20% for some sources, but the effects of source variability may cut that level in half for contemporaneous comparisons. Our results indicate that simple models---ones that scale a fixed polarization fraction with frequency---are inadequate to model the behavior of these sources and their contributions to polarization maps.
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