From my understanding...no
now there is a DNA test but because of crossing breeds back in the past to make the American Pit Bull Terrier, from my understanding you would land yourself with a long list of just about everything.
From my understanding is every breed, when going back to the start, started as a what we would call a mutt. Then specific mutts were bred to meet the standards of what they want. So truthfuly there really is no way or testing that.
Though, my source could be wrong, I have been wrong before, but I really dont think they can do that. So lets see if there is anyone more knowledgable about this topic then I am. This is just my two cents