John Burns, 45, mouthed off at officers when they stopped his car for a routine check on Duchess Place in Rutherglen.
He told one PC he was "going to Raoul Moat him" and made a gun gesture with his hand.
Burns - who claims to be a Scottish Sovereign who believes he can "opt out" of abiding by certain laws - continued his tirade of abuse calling the officers "wife beaters".
Burns, from Mount Vernon in Glasgow's East End, denied shouting, swearing and acting in an aggressive manner on October 24, 2012, repeatedly making offensive and abusive remarks and threats, but was found guilty.
He was also convicted by Sheriff William Wood at Glasgow Sheriff Court of making a gun gesture with his hand.
The sheriff told him: "That's not an expression of free speech, that's abusive conduct to be deplored."
He was ordered to pay £750 within three months or serve 28 days in prison.
Sheriff Wood dismissed Burns' claims the court had no jurisdiction and him not consenting to the proceedings. Outside the court Burns said: "I'll do the time, I'm not paying the fine."
In evidence PCs Iain Leighton and David Dooher told how they stopped Burns' vehicle as part of a routine check.
PC Dooher said that when Burns was told it would only take a couple of seconds he replied: "I will give you one second".
Burns told them that Moat and Cregan are "heroes" to him and said: "Anyone who kills a cop is a good man".
Moat shot three people including police officer David Rathband in Newcastle in 2010 and Cregan lured PCs Nicola Hughes and Fiona Bone to a hoax emergency call in Hattersley, Greater Manchester where he shot them dead in 2012.
Burns became an internet hit when a video of him and two police officers engaged in banter at the side of the road after they pulled him over, was posted on YouTube.