Everyone says you need an argy trap to knock one out but they aren’t actually that fast in the wild, yesterday i tamed a lvl 120 without a trap but I would recommend having at least 150% movement speed just to be safe.
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.