ARK: Survival Evolved Wiki

Less deadly than other arrows, but rapidly increases the victim's torpidity.
— In-game Description

The Tranquilizer Arrow or Tranq Arrow is the advanced ammunition for the Bow (or the Crossbow and Compound Bow). They deal less damage to animals but raise their torpor so you can knock them out for taming. (Note tranq arrows take time to build torpor so after a few hits run the dino/creature around then repeat if it does not pass out; This might fire faster than a stone arrow)

Note: after you knocked out an animal you can walk over them in order to collect the arrows that did not break. Although you shot tranq arrows, you will only get stone arrows back. This is because the narcotic you used to craft the tranq arrow is now in the animal and keeps it knocked out.