The Tranq Arrow (or Tranquilizer Arrow) is used for rendering creatures unconscious. It does less damage than a Stone Arrow, but increases the target's Torpor. Tranq Arrows can be used as ammo for the Bow, Crossbow and Compound Bow.
Upon hit, they instantly increase the target's torpor by an amount equal to 200% of the weapon damage and give an additional amount of torpor equal to 250% of the weapon damage over the course of the next 4 seconds. (ex. A standard quality Bow would Cause 40 Torpor damage immediately, with a timed release of 50 torpor over 4 seconds.)
They can usually be recovered by walking up to the area of impact, but will be recovered as Stone Arrows, the Narcotic being expended.
A second arrow hitting the target will not override the torpor-over-time effect of the first arrow, the effects of multiple arrows will instead stack. That means it's not necessary to wait in between shots to gain the maximum torpor. On the other hand, the torpor increase takes 5 seconds. So if the creature is near unconsciousness, it's better to wait after each shot as to not harm the creature unnecessarily.
A Tranq Arrow fired from a Crossbow is more effective in terms of both damage and torpor when compared to either a Bow or Compound Bow.
However, bows allow Tranq Arrow to be delivered in a quicker succession compared to a crossbow.
Flying creatures take 1.5x damage from non-bullet ranged weapons. This bonus stacks with the 2.5x bonus from head shots.
In Survival of the Fittest, Tranq Arrows become available at level 10 (along with Bow), and can be crafted by using 5 Narcoberries instead of Narcotic (to prevent the need for a foundation, mortar & pestle, and spoiled meat).
You can collect tranq arrows from killing higher level dinos.