It's usually takes about 10 to 30 tranq darts to knock out a rex so you shouldn't use tranq Arrows unless it low level and desperate. And it also takes 10 to 100 narcotics to keep it asleep until you tame it
The easiest thing to use to tame it is prime fish 🍖.
So get a shark first and finally the best tip of always over prepare and use more tranq darts than necessary.
The best place to find a Rex is on the volcano in the middle of the map.
If you use the bear trap strategy which is if you lead it into a Dino gateway that is shaped in a triangle and with a bear trap in the middle (Large Beartrap) and when it is stuck you must put a dinogate behind it to trap it and then knock out.
The Rex are very slow . Put a stone gates around him while he is stuck and use a bear trap then put the x3-x4 stone gates then tranq him out . Make sure you clear the area before setting the bear traps others creature can spring it and u would be left with using your self or a tanky dino for a distraction