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.
If you want to tame one in a safe area, aggro it with a pteranodon (because they are faster fliers than argents) and lure them to a safer area
ex. Empty Beach area. Be sure the argent is close behind you by flying slowly and when it gets a little too close, speed fly a bit then slow down, this also saves stamina. The argent might lose interest every so often but then just turn back and aggro them again. Once you reach the area, land the pteranodon, let the argent get close and tranq it
EASIEST WAY TO TAME AT ANY LEVEL:
Stock up on trans, 4 - 5 per bird, wait for it to land, walk an aim-able distance away, FIRE AWAY, when it comes close, run towards it while flanking from the side and from behind as it passes, you WILL take a foot or two, so be prepared to have SOME food handy for yourself.
They stay tranqed for a little over 30 minutes. Use that time to starve them whil you hunt some predator or big game to get some prime and VOILA!
I solo play and just tamed 5 Argen in one go. I am going to paint them blue and call them The Blue Angles. 😉
If you have one of these get a raft, build a taming pen on top and a space for landing and you have yourself a good portable taming base for anything it can pick up. I've tamed loads with this. It's easier than flying all the way to base or making several taming pens at different locations.
I always find the easiest way to k.o them is pulling them to the top of the volcano and running towards its feet fired darts or arrows. At the top when they attempt to run away they don't really fly up.
If you find one and you have a quetz with a platform saddle, Put the quetz on passive and start shooting the argie. At some point it will fly off and if it is high enough fly below it and shoot it 1-2 times and try to catch it if done right you can takes your tame anywhere!
If u r a ok tribe just have something with about 2.5k health (depending on the lvl or the argy) sit is a area then let the argy attack it while shooting it this is your best bet if u dont have a cage. I did this with a 150 argen.
Make a pen 6x2 dino gateway and a couple of rows of doorsways (no doors),leave one wall tile out. Get Argi to follow you back to pen on pteranadon stop at pens gateway,wait for Argi to hit you fly out missing wall tile straight ahead (at a sprint speed otherwise you'll get stuck), once out park bird right infront of Argi....run round and close gate. Better to build this just out front of base incase it goes to attack dinos but also makes it a nice close and safe tame. Good luck
If you are willing to tame an Argentavis do not keep on shooting it with darts or tranqs otherwise it will die. So shoot it and wait about 5 seconds before shooting it again to prevent it from dying. Do not tame an Argentavis on Carnivore Island as it will get eaten.