Tommy Sheridan was arrested at Faslane Naval Base on the Clyde during a demonstration in February 2002.
He was fined £200 for breach of the peace at Helensburgh District Court in August 2002.
After refusing to pay the fine, an arrest warrant was issued.
Mr Sheridan reported to Govan Police Station in Glasgow shortly after 2200 BST on Sunday, expecting to spend the night in custody.
Before handing himself in, he said: "Nuclear weapons are a crime against humanity and should be removed from the Clyde and from Britain.
"It is the duty of all peace protesters to make a stand against nuclear weapons.
"Politicians in particular should be at the forefront of the nuclear disarmament campaign.
"If we spent our money on pensions and hospitals instead of nuclear bombs, our society would be a much better place to live."
The Glasgow list MSP was due to appear before Glasgow Sheriff Court on Monday where he faces being jailed.
Earlier he said: "I refuse to recognise that opposition to the inhumanity of nuclear weapons is a crime.
"The real crime against humanity is the existence of nuclear weapons and it's the duty of all socialists and those who want to contribute to a more peaceful society to do what they can peacefully to oppose nuclear weapons.

"Prison is an unpleasant place but we have to all make a stand at some time in our lives."