Research studies fail to prove a consistent link between cell phone use and brain cancer. Cell phones emit radiofrequency energy which is a form of non-ionizing radiation, unlike ionizing radiation used in x-rays and CT scans.

The largest study to date of long term cell phone use (Interphone study) found that cell phone use actually reduced the risk for brain tumors. In a small portion of the study, participants with brain tumors reported that they spent longer time on their phone, but other studies that reviewed phone records showed no difference. Most of the media coverage has been due to the International Agency for Research on Cancer (IARC) recent classification of radiofrequency energy as "possibly carcinogenic". Despite exponential growth in cell phone use over the past 30 years, there has been little change in the risk of brain tumors.
 
(http://www.cancer.gov/cancertopics/factsheet/Risk/cellphones)