The easiest method ive found to tame a rex is to lure it into a taming pen made of stone dino gates. Lure with a flier or on foot by closing the gate furthest from the gate you entered from. Then close the gate behind the rex. ( yes rexs can walk through dino gates! So doors are nessisary) then shoot from a safe place till knocked out. Always bring extra tranqs with you and delay shots with tranq arrows to prevent killing the rex by accident. If useing a flier, argies have always worked best for me. Their extra health and slow pace keeps the rex on you as they quickly lose interest and go for whatever else is nearby. The starve method is the safest to prevent spoilage of whatever food source you use.
I have figured out a new way to tame dinosaurs cut off the dinosaurs meat wise in the area try and keep the dinosaur in the area and send a dodo bird out to attack the tea Rex with bunches of Botox in and it had the tea Rex eat the Botox and it’ll knock it out you go feed it meet make sure you have plenty of Botox in and you’ll have a pet your ex and no I would not recommend trying this whenever your level one side effects may be dead dodo bird hey might find you and run but seriously You better find a good hiding spot