Are radiologists likely to get cancer because of their exposure to radiation?

No!: They might, if they didn't protect themselves. But they go behind leaded glass, they wear lead aprons, and they stay in their offices while other people take the x-rays (who also protect themselves). No risk whatsoever.

In the early: days of radiology, little was known about the long term effects of radiation, and many xray workers and doctors ended up with cancers. Nowadays, exposure is minimized by safety equipment and improved technology. Radiologist xray exposure is monitored on a regular basis with badges and other detectors.

Potentially: Yes, if the radiologist has not appropriately protected him/herself from radiation in the workplace, this can increase their long-term cancer risk.

No: No radiologists and other staff are well protected by lead shields, also also their exposure to radiation energy is annually measured from their badges. Only way they can get exposed is if they careless and break down in required techniques.