RF is nonionizing radiation, meaning that it isn't energetic enough to knock electrons off of individual molecules. Obviously it's impossible to say "it can't cause cancer" with 100% certainty, but in all the studies that have been conducted on RF over the last 70 years, there has never been any indication that nonionizing radiation causes an increased incidence of cancer.

Ionizing radiation (X-rays, gamma radation, etc.) is on the other side of the electromagnetic spectrum relative to visible light. These types of radiation are energetic enough to interfere with and ionize molecules, such as your DNA. This can directly lead to cancer.

The only thing dangerous about RF is that if you disperse too much RF energy into something (ie. your body) it usually comes out as an increase in temperature or as an influx of electrical current, which can cause internal/external burns, etc.

Source: mandatory yearly IEEE mandated RF safety training

Well, I don't know your Mom, but the answer is 'yes, but 0.0001% less risk than either the sun or time'.

Of course, I'm going by the moto here that 93% of statistics are made up on the spot.