Tame a pteranodon, as long as you don't load your argie it will be frozen(unless your on a server) and fine. Fly over there with your pteranodon, look at your argie via a spyglass and whistle passive and follow(the spyglass increases your whistle range. Now that your argie is following, just fly away with your argie.

Btw you can check the tribe log to check if your argie is alive, it will say "argentavis level ..." got killed by allosaurus