Radiation can produce mutations in our DNA, wich means that the genetic information is altered and our cells can start misbehaving and generate cancer. However, phone radiation is very very weak, and mutations due to this are very very small, so the answer is 99.99% no. A mixture of factors can give rise to cancer, and phone radiation could be one, but most probably the least important!
It’s a real problem work this out. Some things in life have a tiny tiny tiny effect to cause a disease and so you can’t tell if it causes a disease unless you do an enormous study. The radiation with phones is likely to be very weak and so doesn’t drive cancer as strongly as sunlight for example.
I think that the evidence is telling us that phones are pretty safe