Q.Damage to my orange tree possibly caused by rats.
Is there something that I could maybe wrap around the trunk of my orange tree that would stop the rats from climbing. I can only use rat bait sparingly as I can’t risk my dog getting in there.

Most bark damage should be left uncovered and allowed to heal naturally.
You should however prevent further damage. A wire cage formed around the bottom of the tree may help prevent further damage. This should be used to keep the rodents from reaching the tree. Do not attached the fencing to the tree. If it is rats, you will need a wire fencing that they can't squeeze through.
Here are articles that have more information.
https://www.gardeningknowhow.com/plant-problems/pests/animals/eliminate-rats-in-gardens.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/repairing-tree-bark-damage.htm