When you see one, put any kinds of berries in your last inventory slot and walk up to them slowly. They will take the berries and it will add to their bar. Just keep doing that over and over
-bboss505 (pls up-vote

If they swipe berries off of you, they have the potential of taming themselves! This just happened to me! Now I have Peggy.

so i was playing ark few days ago, i was running around and he just jumped into my face and window for naming just showed. it was so random

Make sure you have nothing on you besides loads of Mejos, get the Pego in a taming pen and let it steel the Mejos from you.