Get it in a cage find a near by animal to kill drag the body over to the argie and knock it out while it has the green buff on its head it will knock out with 0 food and instantly tame. It’s advised to shoot it before you feed it the body or have help from a friend considering the green buff on their head is only a couple seconds long but definitely worth the effort
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.