The former National Security Agency intelligence officer agreed to stand after a request to his lawyers by students from Glasgow University.
Mr Snowden now lives in Russia after fleeing America, via Hong Kong, in May having leaked extensive internet and phone surveillance by US intelligence to the media.
Student Chris Cassells, who is helping to run his campaign, argues the nomination gives students the opportunity to show both support for his actions and disgust at the security services.
However, there has been opposition to the nomination on social networking sites such as Twitter and Facebook and last week campaign posters were slashed and cut up.
Responding to the vandalism, a statement on the Facebook page dedicated to Snowden's campaign states: "It is deeply disappointing that a small number of people, for whatever reason, seek to stifle what should be a colourful and exciting atmosphere in the run-up to the election."
In addition, a number of campus organisations, including the historic Glasgow University Union, have decided to campaign for a rector who will to work actively on behalf of the students, rather than one who is absent.
The three other candidates for rector - cyclist Graeme Obree, author Alan Bissett and Scottish Episcopal clergyman Kelvin Holdsworth - have all been campaigning at the university and see themselves as able to fight for student causes.
Jess McGrellis, president of the university's Student Representatives' Council, said opposition to Mr Snowden in recent days had been unexpected.
She said: "I have been surprised by the backlash against him. Even among students he is quite a controversial figure and we have got a lot of international students who may not agree with what he has done.
"It also became apparent at the hustings the Snowden campaign did not have a great deal to offer in the detailed discussions and that was very telling, but he will still be a popular choice."
Stuart Law, president of the Glasgow University Sports Association, which is backing Obree, said the university needed a working rector and that message was getting through to the student body. He said: "The hustings this week were surprising because it seemed a lot of people were very adverse to the idea of having a non-working rector.
"The rector position goes back to the 1400s and in that time there have only been about five times when someone has been elected as a political statement. It is not a tradition of Glasgow University to do that. A working rector is important for the students because it is an extra voice on the university court."
However, Mr Cassells said the overall response to the campaign had been positive. "We have never pretended Snowden will be a working rector," he said.
"We have had non-working rectors in the past and we already have student representation through other bodies, as well as direct student movements."
The new rector will be announced on Tuesday after two days of voting.