On carnivore island on the island it gets stuck pretty easily. Easy to lead into trees to get it stuck just make it follow you to the tree area. I hit it twice with Tranq arrows then went in with my frog and used its topor attack easy tame. The hard part was protecting the tame for the time nessesary to tame it.
Resource intensive but easy and flexible trap to tame any (and many) rex:
1) Get a wooden raft
2) Place stone foundations 3 by 3 to make your raft indestructible by rexes (look up dropped raft foundation on utube to get the 3x3, it takes 10 seconds). You can also use a hatch frame over the rudder to still drive.
3) Fill in all sides with empty stone doorframes 2 high
4) Add wood ramps up the front of the boat so the rex can walk over to get in
5) Park the boat anywhere near rexes, lure your favorite into the trap and tranq through the open walls from safety, the rex can’t get out
Now you have an easy and mobile rex trap that works for plenty of other dinos too :) I’m not sure if you can drive around with the rex while it’s unconscious, but you can always build a couple spike walls to keep other dinos away. Enjoy my favorite trap in Ark and have fun with free rexes!