Its possible to tranq it out with out a taming pen. I did it with just a crossbow and a pteradon. I shot it a few times in the head and kept distance by flying away until it started to run away. Then i followed it and shot it and so on until it was down. In a taming pen it would be easier but if you want to do it without i wish you good luck. I tamed 2 100+ with ease my way at the same time.
1-2 tranq darts in head and he’s knocked, go get some meat and kill some of those jellyfish and get bio toxin then put the bio toxin in it and feed it until the argies hunger is on 1000 or less then put all your meat in it
If you need an argy and don’t have time to tame one with a trap, just go to carno island, kill a Dino in front of an argy and let it harvest its body. When the green health icon shows up on top of it, knock it out with tranq arrows and the argy is instantly yours.