No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
if concerned check some local banks online and see what rates they offer and see how you compare.
Can you find lower, YES.
Would you qualify? Who knows.
How much lower could you have gotten? I would say 3.9% is the lowest I have seen, so you are at a desirable margin.
Its not a new car.
Used cars traditionally have higher interest rates than new.
Realistically you got a darn good rate and should be happy with it. Even if you have Bill Gates credit you should be happy.