Online voting opened yesterday and will run today, with the result expected this evening.
Four candidates have been nominated, including former National Security Agency intelligence officer Edward Snowden. He now lives in Russia after fleeing America, having leaked internet and phone surveillance by US intelligence to the media.
Chris Cassells, who is helping to run his campaign, says the nomination is a chance to support his actions.
Cyclist Chris Obree, clergyman Kelvin Holdsworth and author Alan Bissett are the other candidates to replace outgoing rector, MP Charles Kennedy.