About 10 or 15 years ago it was noticed that the radioactive gas radon was prevalent in basements in areas where the underlying rock is granite. According to EPA rules, many places have more than EPA considers safe, and EPA advocates mitigating it, e.g. by sealing basements. Bernard Cohen compared death rates from lung cancer in elderly women in counties where there is lots of granite with the death rates where the underlying rock does not emit radon. He found no increase, suggesting that the linear hypothesis exaggerates by at least a factor of 4. From potassium in the blood.
Potassium is essential for life, but it contains a small fraction of a radioactive isotope.
It would be difficult, but perhaps not impossible to tell whether this natural radiation within the body contributes to cancer. The largest average human exposure to radiation is from medical X-rays. As part of radiation treatments for cancer, people are sometimes exposed to radiation up to where they get acute radiation sickness. If they survive the treatment and survive the cancer, they don't seem to get additional cancer from the treatment. Here's a table from the School of Public Health at the University of Michigan.