Best way to tame is to build a small cage with pillar walls that it can’t fit out of but you can (add roof). Make sure to add in a dino gate so that it can get in. Once it’s in, close the gate and run out. Tranq it from the outside but careful not to kill 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.