Best way to tame is make it follow you to a taming cage with a dinosaur gate and door frames as walls so you could walk out once inside close the gate now go kill something and drag the body to it once it's eaten the body you should see green light coming from the bird that's when you quickly shoot it with trank arrows and it should almost instantly tame ...just try it
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.