Generally not. Most radiation producing machines are labelled that they must be used by or under the supervision of a physician. Hospitals will grant privileges for doctors and will generally allow the use of fluoroscopy, but anyone using these machines are monitored.
See below. It is state dependent on whether a physician requires a special license to use fluoroscopy and what obtaining one entails. There is no requirement of fellowship for use of fluoroscopy as the use and interpretation is learned as a student and resident and is somewhat similar to use and interpretation of plain film radiographs with some minor variances (ie ability to gather live images).