The former contractor for the US National Security Agency (NSA), who is in hiding in Russia, is standing against cyclist Graeme Obree, writer Alan Bissett and clergyman Kelvin Holdworth.
A group of students at the university said Snowden had accepted their invitation to stand, which was made through his lawyer.
The group said Snowden's candidacy is an "opportunity to show our gratitude to a brave whistleblower, and thus to all other whistleblowers".
"All nominees have personally agreed to take part in the election" of the new rector on February 17 and 18, the university said in a statement.
The post of rector mainly involves representing the university's students. The successful candidate is expected to attend meetings with the governing body and other authorities.
Previous holders include Winnie Mandela and Israeli whistleblower Mordechai Vanunu. The current holder is former Liberal Democrat party leader Charles Kennedy.
Snowden received temporary asylum in Russia in August -- a move that infuriated the United States -- and is believed to be living in the Moscow area.
In an interview with the New Yorker published Tuesday Snowden rejected suggestions he was a Russian spy, saying he acted alone in exposing US surveillance programmes.