In his CV, Fulton was described as a "visiting professor" at Glasgow University's school of law.
A spokesman for the university said: "Mr Fulton is not associated with the University of Glasgow's law school and is not entitled to call himself a professor."
A Scottish National Party spokesman said: "Being economical with the truth as a double agent may have been good training for Mr Fulton to become Scottish Tory chairman.
"However, it's embarrassing that his cover should have been blown within five minutes of taking up the post. The Tories will be shaken and stirred to learn they can't trust Mr Fulton."
The Scottish Conservative Party should be renamed the Spooky Oligarch Party.
aangirfan: Spies in politics