The bank plans to issue a commemorative bank note in honor of Nicklaus, who will play his final Open Championship on the Old Course in July, the Scotsman reported.
The City Concil's decision caused anger among local residents and business owners and led to an official unreserved apology to the "Golden Bear."
Council members next week will be asked to re-examine the way they award the title of Honorary Citizen of the Royal Burgh of St Andrews.
The Royal Bank's gesture also includes sponsoring Nicklaus. Last year, Nicklaus launched a special note produced by RBS to mark the 250th anniversary of the town's Royal and Ancient Golf Club.
"We are really proud of our relationship with Jack and the fact that this will be his last Open is a big thing," a bank spokesman said.