We present HD-TESS, a catalog of 1709 bright (V~3-10) red giants from the Henry Draper (HD) Catalog with asteroseismic measurements based on photometry from NASA's Transiting Exoplanet Survey Satellite (TESS). Using light curves spanning at least 6 months across a single TESS observing cycle, we provide measurements of global asteroseismic parameters ({nu}_max_ and {Delta}{nu}) and the evolutionary state for each star in the catalog. We adopt literature values of atmospheric stellar parameters to estimate the masses and radii of the giants in our catalog using asteroseismic scaling relations, and observe that HD-TESS giants on average have larger masses compared to Kepler red giants. Additionally, we present the discovery of oscillations in 99 red giants in astrometric binary systems, including those with subdwarf or white dwarf companions. Finally, we benchmark radii from asteroseismic scaling relations against those measured using long-baseline interferometry for 18 red giants and find that correction factors to the scaling relations improve the agreement between asteroseismic and interferometric radii to approximately 3%.