While the candidate himself continues his battle to claim asylum in Russia, students at the university have made international news by securing his name on next month's ballot.
They say Mr Snowden - famed for his decision to leak classified security files from both British and American agencies - embodies the fundamental pillars of democracy and public rights.
Howard Liley, one of the men behind the campaign, said: "Edward Snowden, if elected, will join a long list of people who have stood up for their beliefs and have received the recognition of our institution for doing so.
"By campaigning for Snowden's election as rector, the message we want to send to the students of the University of Glasgow, and people all over the world, is that they should not be afraid to call into question the practices of governments and organisations."
The elections are on February 17 and 18, with other candidates including Graeme Obree, writer Alan Bisset and the Very Rev Kelvin Holdsworth.
Yesterday, Mr Snowden said the US National Security Agency was involved in industrial espionage and would grab any intelligence it can get its hands on regardless of its value to national security. His legal adviser said he would be willing to talk with US Attorney General Eric Holder about returning to the US but only with a guarantee of amnesty.