If you want to tame a rex i reccomend going to the carno island

Reason: it has one of the best and most frequent rex spawns+ has alot of argentavis+ carnos for constant prime meat source

You need 4 stone dino gateways

Place three in a U shape and a large bear trap in the middle

Bait the rex on foot its not faster than you and you can step on the large bear trap it dosent affect you

Then you have to walk through the gateways and the rex would get stuck inside the trap, then go around the gateways and place the 4th one to make a square with a trapped rex inside

After that you can just hit it with tranq darts and a crossbow (leave 4-5 seconds between each arrow) and dont forget to feed it prime meat from the argentavis and carnos on the island

You got an easy free rex😎