Taming a terror bird won't be easy because they come in packs of 3. So if you want one of them just kill the other 2 and tame the one you want. Mainly to tame one you'll need bolas, tranq arrows or a club to knock it out. Its preferred kibble or raw meat works faster and mutton.
BEWARE THEY ARE LEARNING!
Not only did one kill my me and Parasaur mount (we never stood a chance), my computer froze trying to respawn. This is the first time Ark has crashed my computer. I’m convinced the Terror Bird did this. They are learning how to terrorize us outside the game. AVOID AT ALL COSTS BEFORE THEY ESCAPE THE MATRIX!