Narc it up to 75% Torpor and check with the magnifying glass to be sure. Feed it a corpse(fish or dodo or smth), and as soon as it eats the corpse, narc it out! It will heal up and when its narced its food will drop 2000-4000(depends on how fast you narc it out). TADAA...instatame ;)
An argentavis can't fit through a ceiling with one tile missing, but a pteranadon or lymantria can. Build a trap with one corner ceiling missing, aggro the argentavis, fly in one side and out the missing ceiling tile, and land. Dismount, run around, and close the entry door. Tame safely at your leisure.