Best to do a 3x3 stone foundation and 81 normal stone door frames make sure the door frames are 3 high and just make a normal stone dino gateway and some gates. Keep it distracted with a dodo in the cage so you can close the door. I recommend using bio toxin if you live near or in the beach since narcotics are really important for tranqs. Monitor the argy always. You can get a female and male to reduce your struggles in taming more. Just mate them. PS: Argies are great for taming the giant bigfoot things since they can pick it up. Mobile player here just got another baby argy
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.