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

More Argentavis Taming & KO Tips