Tobacco plants appear to neatly absorb the element from air and soil. In addition, tobacco growers have frequently relied on fertilizers enriched with phosphate by the mineral apatite, which often comes in tandem with radium, (Ra), an element known to decay to polonium-210. U.S. tobacco companies have known this since the 1950s; an industry study done in the 1960s showed, for instance, that filters do not remove radioactivity from tobacco smoke. As documents released through legal settlements showed, tobacco companies managed to conceal this risk from the public until the 1990s.
And risk is definitely the right word here. For a heavy smoker — say one smoking a pack-and-a-half of cigarettes a day — some studies estimate that the radiation exposure is equivalent to 300 chest X-rays a year. There are also scientists who believe that polonium-210 is the primary risk factor for lung cancer in smokers — not to mention low-level radiation sickness. It’s thus not surprising that after the poison was discovered on Arafat’s clothes, questions were raised about whether this could be just be evidence of cigarette exposure. After all, the Palestinian leader and many of his colleagues were known to be smokers
http://www.wired.com/wiredscience/2012/12/yassar-arafat-and-the-radioactive-cigarette/
I’ve seen Arafat smoking in some doco as well