There are those who think so. The thing is, cell phones operate on radio frequencies. The human body produces higher energy radiation than radio (i.e., infrared). Visible light is also higher energy than radio. In fact, you have to go to ultraviolet before you get electromagnetic radiation that affects human cells -- specifically, sunburn.
In this article, the researcher also talks about "electromagnetic fields" -- that bogey man from the late 80s. They've been shown again and again to cause no harm, but some people just can't let it go.
I can think of lots of reasons to turn off your cell phone. Cancer isn't one of them.
(Thus ends a glimpse of my day job.)