You are always subjected to a low background of ionizing radiation from a number of natural and artificial sources, which include cosmic rays, trace amounts of radioactive nuclei in the air and in food, and indeed from the ground. A good place to read up on this is the corresponding Wikipedia article.
The radiation from the core, however, has no chance of making it to the surface. Gamma radiation is typically stopped by a few to maybe 20 or 30 cm of rock or soil. (There is also the danger that material used to shield against gamma radiation becomes radioactive itself, but of course this is hardly an issue with the Earth's core.) Alpha and beta rays are even easier to stop. Trace amounts of radioactive nuclei, though, can be present in the soil and buildings around you and will then expose you to a small amount of radiation.
It's important to note that this is natural and nothing to worry about. The most significant contribution to background radiation, away from zones like Hiroshima, Chernobyl or Fukushima, is the trace amount of radon in the air you breathe.