This has been said before but I'm writing it a tad differently than top comment, this is the method I use in solo play. These are a very easy tame if you have any type of fabricated weapon. Find an Argy that's away from the group, aggro it, then kill something else with a sidearm or assault rifle while it's attacking you, get near the dead body and when it attacks you (and hits the carapace) it'll get green health buff above it's head.
To tame one easy all you have to do is kill something so the argent Avis can eat, and while it’s healing you must knock it out with tranq arrows or darts. If it is knocked out while healing it’ll starve immediately and it’ll tame in seconds no matter what level!
If you lose your argys go to the place that shows your character press the tames button which says how much animals you have, Look for your argys name press request, then wait. It will tp to you, if it’s alive.