A easy and cheap way to tame is using 3 stone fence foundation and 6 stone doorway plus a door. You make it into a u shape and lure rex in then close the door and tame it up. For mobile as the door auto close I recommend using another fence foundation and 2 doorways to block of the exit/entrance you can also try pillars.
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
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.
Stay high up and knock it out then make sure to have plenty narcotics put in creatures inventory and don’t put any meat in inventory access states at check hunger wait until it’s hunger is low while feeding it narcotic when hunger is low put any meat kind at it will start to tame fast.