To tame kill a dead creature near one. Something like a high level ovis is good. The Fjordhawk will come to the body, eat it and its taming effectiveness will rise. Remember to use sanguine elixir from the desmodus. These cool birds will bring your stuff to you when you die and are invincible while on your shoulder. They look cool but you can't put another shoulder pet on your shoulder even though the hawk is on the other side. You can see bags on the floor and how weak dinos are like with a direwolf.

I named mine hawkeye