Unlikely. If you're not scared of all the non-radioactive poisons in cigarettes, you're not gonna be scared from the radiation. According to this, about 360 µSv each year for a pack a day smoking. Comparative things are in the green section, e.g. yearly dose from potassium in body.
It gives an effective dose of 252 μSv per year, which according to the chart puts it in the green section. Right around the EPA’s yearly release limit from nuclear power plants, but below what you’d get from your bodies own natural potassium or even getting apparently a single mammogram. Not good, but I guess not horrible, though I imagine it adds up over time and the harm from cigarettes may be more chemical than radioactive. Smoking isn’t worth it.
"In a person smoking 1 1/2 packs of cigarettes per day, the radiation dose to the bronchial epithelium in areas of bifurcation is 8000 mrem per year -- the equivalent of the dose to the skin from 300 x-ray films of the chest per year. This figure is comparable to total-body exposure to natural background radiation containing 80 mrem per year in someone living in the Boston area."
8000 mrem is about 80 mSv.
A lifetime of background radiation in a year, so quite high.
Even the most basic mammogram includes about 4 exposures to the radiation source. It's not as many pictures as a CT scan, but it's still comprehensive and some of them act like pseudo-CT scans.