Campaigner Mick Napier has put forward a petition to Holyrood calling for Mr Snowden to be offered political asylum now, conditional on the outcome of the vote in September.
The former university lecturer made his case before MSPs on the Public Petitions Committee.
Mr Snowden, who is staying in Russia where he has been given temporary asylum, became a wanted man when his leaks brought to light secret National Security Agency (NSA) documents which revealed widespread US surveillance of phone and internet communications.
The petition comes after the whistleblower was elected Rector of Glasgow University earlier this year.
Mr Napier told the committee that Mr Snowden was owed a "debt of gratitude" for his actions and it would be an "honour for Scotland" if he was to come to the country. He called for the committee to push the petition "as vigorously and as quickly as possible".
Several MSPs were sympathetic to Mr Napier's campaign but agreed to defer further consideration until after the referendum.