Yes. X-rays and gamma rays are known human carcinogens (cancer-causing agents). The evidence for this comes from many different sources, including studies of atomic bomb survivors in Japan, people exposed during the Chernobyl nuclear accident, people treated with high doses of radiation for cancer and other conditions, and people exposed to high levels of radiation at work, such as uranium miners. 
Most studies on radiation and cancer risk have looked at people exposed to high doses of radiation in the settings above. It is harder to measure the much smaller increase in cancer risk that might come from much lower levels of radiation exposure. Most studies have not been able to detect an increased risk of cancer among people exposed to low levels of radiation. For example, people living at high altitudes, who are exposed to more natural background radiation from cosmic rays than people living at sea level, do not have noticeably higher cancer rates. 
Still, most scientists and regulatory agencies agree that even small doses of gamma and x-radiation increase cancer risk, although by a very small amount. In general, the risk of cancer from radiation exposure increases as the dose of radiation increases. Likewise, the lower the exposure is, the smaller the increase in risk. But there is no threshold below which this kind of radiation is thought to be totally safe.