Find a safe taming spot within render distance. Shoot your desired argentavis once with a pistol with a scope attached. It'll head straight for you so be ready with a harpoon launcher and net projectile. When in range, shoot with the net and knock it out with tranquilizers of your choice. If its high level and the the net is going to wear off before knockout, toss a tent over it and continue with the tranquilizers.