The nomination of the former CIA agent, who has temporary asylum in Russia after fleeing the US via Hong Kong in May, was arranged by a group of students through his lawyer.
Snowden, who was responsible for a series of major leaks on the extent of British and American surveillance on their own citizens, joins a field with three other candidates including cycling hero Graeme Obree, author Alan Bissett and Scottish Episcopal clergyman Kelvin Holdsworth.
Among the post-holder's key duties is to chair the university court at which all major decisions are taken. Rectors, who serve for three years, are also expected to work with the students' representative council, and to bring concerns to the attention of university management.
Other rectors who never carried out duties include Winnie Mandela and jailed Israeli whistleblower Mordechai Vanunu.
"It's really a matter for the students," said a university source.