Edinburgh Labour councillor David Walker said he had not previously been aware of the level of violence involved in the case of John Lindsay, who was jailed for seven years for the crime.
Lord Turnbull had asked Mr Walker to apologise after he wrote on council notepaper to the judge asking that Lindsay be spared jail.
Craigmillar and Portobello councillor Mr Walker offered his "sincere apologies" to the court.
Lindsay and two accomplices subjected 20-year-old Jamie Alexander to a terrifying 90-minute ordeal in July last year.
The young man had wandered into Lindsay's unlocked home looking for directions.
Mr Walker did not respond to a request for comment but was reported as saying: "I hope those who were desperate to castigate me will think twice next time before commenting on something they know nothing about."