Rat terriers can be hit or miss. Like many breeds they've had a lot of ability breed outta them in the name of the almighty dollar and even before this they were not all created equal. Some had good noses but were more den dogs, some had good noses and tracked well, some only used there eyes and treed well, etc. Your odds of your RT being a world beater hunting dog are slim. Slightly better are the odds of having it be acceptable but odds are very good that you can have a world class hunting buddy that may help some in the woods.
Basically what you are looking at is having the dog tell/show you what it's good for and adapting your hunting to his, not vice versa. It's not like going out and buying a dog to fill certain traits to meet your style. You have no idea of this dogs traits so you'll have to go his way. There are things you can do to help but if that dog just don't have any tree in him you ain't gonna talk him in to it, same with tracking. Advantage, you have is RT and no matter how far away from any hunting breeding they are just dang gamey and like to chase. Turn him loose on some squirrels, maybe some rabbits, see what he does and try to build on that.