The high-frequency radio sky, like the gamma-ray sky surveyed by the Fermi satellite, is dominated by flat spectrum radio quasars and BL Lac objects at bright flux levels. To investigate the relationship between radio and gamma-ray emission in extragalactic sources, we have cross-matched the Australia Telescope 20 GHz survey catalog (AT20G) with the Fermi-LAT 1 year Point Source Catalog (1FGL). The 6.0 sr of sky covered by both catalogs ({delta} < 0circ, |b| > 1.circ 5) contains 5890 AT20G radio sources and 604 1FGL gamma-ray sources. The AT20G source positions are accurate to within ~1 arcsec and, after excluding known Galactic sources, 43% of Fermi 1FGL sources have an AT20G source within the 95% Fermi confidence ellipse. Monte Carlo tests imply that at least 95% of these matches are genuine associations. Only five gamma-ray sources (1% of the Fermi catalog) have more than one AT20G counterpart in the Fermi error box. The AT20G matches also generally support the active galactic nucleus (AGN) associations in the First LAT AGN Catalog. We find a trend of increasing gamma-ray flux density with 20 GHz radio flux density. The Fermi detection rate of AT20G sources is close to 100% for the brightest 20 GHz sources, decreasing to 20% at 1 Jy, and to roughly 1% at 100 mJy. Eight of the matched AT20G sources have no association listed in 1FGL and are presented here as potential gamma-ray AGNs for the first time.We also identify an alternative AGN counterpart to one 1FGL source. The percentage of Fermi sources with AT20G detections decreases toward the Galactic plane, suggesting that the 1FGL catalog contains at least 50 Galactic gamma-ray sources in the southern hemisphere that are yet to be identified.