I have an old 1909 Germany 30-06, I was wondering if it possible to add rifle scope on it?

Yes, any mount designed for a 98 Mauser will work on a 1909. The fact that it is .30/06 is a different matter. These were originally in 7.65x53 Mauser. To make them sell better, the importer rechambered them to .30/06, a cartridge that has the same base dimensions, it is just a longer case. HOWEVER, the bore diameter is still .312 or thereabouts, and a .308 diameter bullet isn't likely to shoot that well. It is a SAFE conversion, but not a real desirable one. Most of the converted rifles I have shot average two to three inch groups at 50 yards, not great accuracy by any standards.

Ok Thanks for reply it back. So any rifle scope will fit. It has metal piece on top of the rifle where I can adjust the sight from 200yds to 2000yds. Do I have to take that piece off before I put on the scope?

You actually happen to have a highly desirable mauser action. It's been used for conversion to all sorts of cartridges including some dangerous gasme cartridges like the 505 Gibbs. It's expensive to do that but to rebarrel to things like .240 Weatherby all the way to .338-06 is not too terribly expensive. Consider a rebarreling

Now to answer your question.....NO...you don't have to remove your rear sight.