You'll need to wait until you've got Bolas to tame or kill this, as Parasaur are too fast to be outrun at base Movement Speed. Once it's Bola'd, just hit it with your Club or Slingshot. Parasaur Taming is a lot like Dodo Taming - just shove berries down it's mouth.

When tamed, a small group of Parasaur make a great protection against Raptors. They are also a lot better than you at harvesting berries. Late game, Parasaurs can be put in Turret Mode so they can tell you when your eggs have hatched.

More Parasaur Taming & KO Tips