Depends. MRI itself is safe, but they often add "contrast" which is known to cause cancer (I'm not clear on if there is more than one choice for contrast though, or if they all cause cancer). Of course contrast is mostly used when they looking at a something - likely a tumor that might or might not be cancer to decide how to treat it - in that case does it matter that your long term cancer prospects go up when without it your short term prospects are not good.
There is no compelling evidence that MRI contrast agent causes cancer. Gadolinium (the stuff that’s in the contrast agent) can deposit in the body, e.g. in the brain, but if this even has any consequences is still unclear. Nonetheless there is some nice research going on how to drastically reduce the amount of contrast agent needs to be administered through image postprocessing.
Hmm. When I check a few years ago what looked like authortive people said it was - I will admit to not being an expert though.