One quick check is to make sure your der cable is not too tight. If you rotate the der barrel 1/4 turn clockwise, does that make it better?
I agree with the others that it's more likely to be old or guncked-up housing and cables, but the barrel adjuster is so easy to try. If you take the rear wheel out, does it still move the der slowly to the right? If so, go for the cables/housing.