To give you the short answer: Yes. As well as the chair you are sitting on, the air you are breathing every day and the soil you are standing on. Basically everything in nature has some level or radioactivity. However, the radioactivity of granite (or your chair) is not so high that it could produce any harm.
A more cientific explanation is that there is the so called External Exposure to radioactivity of every human being. The level of the External Exposure is about 0.7 mSv/a. It is composed by the radioactivity that hits the earth from space and from the sun (cosmis and solar radiation), and by the radioactivity of small quantities of radioactive elements almost anywhere around us.
The cosmic radiation is of aproximately 0.3 mSv/a, while the radioactivity of the environment is of about 0.4 mSv/a. For more detailed cientific information see for example this study by the GSF-National Research Center for Environment and Health at the Technische Universität München.
The radioactivity of all the materials around us comes from tiny quantities of mostly uranium that is inside of almost any natural material. Sedimentary rocks (like sandstone for example) contain about one to four micrograms of uranium per gram of rock. Igneous rocks (that is basalt or granite) can contain between 0.5 to four micrograms of uranium per gram of rock. Sounds quite a lot. However, usual sand (like beach sand for instance) contains about three micrograms of uranium per gram of sand. And the average soil contains one to three micrograms of uranium per gram.
The radioactivity of granite and marble is therefore not higher than the radioactivity of any other natural object around.