There is not enough evidence to say one way or another that non-ionizing microwaves at the energy emitted by cell phones can cause cancer.
I can think of a mechanism that may lead to cancer, however. Ultraviolet radiation (non-ionizing) can obviously cause melanomas. Even though radiation may not be ionizing, it can at the right frequencies cause rotational and vibrational oscillations in molecules. That's why microwave ovens heat water.
I would think that at the right frequencies, telomeres at the end of DNA could be stressed to the point that they break off causing premature aging in a cell and possibly cancer during replication of a cell that has extensive damage to telomeres.
From the University of Utah,”How big a role do telomeres play in aging?
“Some long-lived species like humans have telomeres that are much shorter than species like mice, which live only a few years. Nobody yet knows why. But it’s evidence that telomeres alone do not dictate lifespan.
Cawthon’s study found that when people are divided into two groups based on telomere lengths, the half with longer telomeres lives five years longer than those with shorter telomeres. That suggests lifespan could be increased five years by increasing the length of telomeres in people with shorter ones.”
In the case of cell phones vs. microwave ovens, it’s like two watts vs. 500 watts. Think being hit by a bullet at 1 ft./ min. vs. 250 ft./min.