Rat Terriers traditionally chase small vermin which burrow underground, but squirrels are arboreal in nature. Training your Rat Terrier to hunt squirrels will take some guidance on your part, and an adjustment of his traditional hunting habits on your dog’s part. You can teach your Rat Terrier to locate the squirrel, by scent or sight, chase it up the tree, alert you of location with barking, and then hold the squirrel there for you to come along and remove it.
The great thing about Rat Terriers is that they tend to hunt close to their handlers, so they don't miss opportunities to tree squirrels nearby. A far ranging dog may go farther, but is not necessarily covering more ground and may be too far away before the squirrel bolts from treetop to treetop, making a quick escape. Encouraging this close hunting trait in your Rat Terrier is part of making him a good squirrel dog.
Before hunting with your Rat Terrier, you will want to make sure he is used to gunfire so he is not startled when hunting. Other squirrel hunting dogs can be a great resource to teach an inexperienced dog how to look for and chase squirrels, and your Rat Terrier will soon learn to mimic their hunting behaviours. Good obedience and recall is very important, so you can direct and keep your dog out of trouble. Squirrel scent, carcasses, and tails can all be used to motivate your dog and familiarize him with squirrels, as can a live trap squirrel, and a small cage that can be hung from a tree.