It is very crucial that I ask whether it could and not whether it does. I do not mean to be the least controversial.
To my surprise, having read "Physics for Future Presidents" by Richard Muller last year, I've come across a sentence of the sort (I'm paraphrasing):
cell phone radiation is way too weak to effect molecular structure, and therefore any claim about cell phone radiation causing cancer can be attributed to people blaming cell phones for their cancer.
This seems like a very strong statement! Is this a consensus among physicists that there is absolutely nothing to the claim that cell phone radiation could possibly (in any significant way) cause cancer? Is this really just being thrown around because people don't understand the physics?
To be very precise, the question is: is there a physics model that would suggest a mechanism by which cell phone radiation can cause any sort of damage that could lead to cancer?