The short answer is no, there is absolutely zero reputable evidence that GMO foods cause cancer.
Cancer is a name applied to a spectrum of diseases where cells proliferate abnormally. There is no way that the subtle and well-understood alterations of a plant’s genes can cause cancer. There is nothing about the Bt protein (used in insect resistance, also in organic pest control), the EPSPS enzyme (which confers herbicide resistance simply by substituting for the native enzyme in the plant) or the process itself that would induce such cellular changes in human cells that would lead to cancer. It is just not plausible.
Some of the confusion comes from reports where the Bt protein or glyphosate (the herbicide used on some GM crops) is applied to cell lines in a petri dish, and the cells show changes associated with stress and perhaps abnormal proliferation. However, cells in a dish do not behave like cells in the body. Through years of careful evaluation, there is no reliable evidence that GM foods cause the same changes in a living organism.
Quite to the contrary, future plants may be engineered to produce nutrients that fight/prevent cancer or even eliminate compounds that increase cancer risk. One such product is close to commercialization. Potatoes produce a small amount of acrylamide, a potential carcinogen, when heated to high temperatures. A potato has been engineered to not produce that compound, and that leads to safer food.