The businessman, meanwhile, has pleaded not guilty to one charge laid by the SFO under the Secret Commissions Act.
Both men were remanded on bail and will appear in court again later this year.
The alleged bribe was over a technology goods contract for the council, court documents read.
The SFO said in a statement today the goods were USB flash drives from China.
Along with allegedly accepting or obtaining a bribe, Rasila is also accused of inducing or causing another person to "deliver over, execute, make, accept, endorse or alter" the contract for a pecuniary advantage.
While working at the council he was tasked with obtaining quotes for the supply of the goods from prospective suppliers, court documents read.
It is alleged Rasila prepared an anonymised price comparison spreadsheet and excluded material price information.
The council then awarded the goods contract, relying on the details of the spreadsheet, the SFO claims.
The supply contract was valued at $152,520 and was varied to $140,150, allegedly as a result of the spreadsheet.
Auckland Council chief executive Stephen Town said in a statement earlier this week that there was "zero tolerance for bribery or any kind of illegal behaviour".
He said the council took any such allegations "very seriously, including a commitment to investigate all instances where any such activity is believed to have taken place".
All council staff, he added, are trained on the principles embedded within the council's charter, which sets out the expectations for staff conduct.
"This also includes a responsibility for staff to speak up if they suspect any wrongdoing."
Town said the accused former staffer left the council three years ago after the alleged offending occurred.
"Despite our disappointment that a former employee of ours is now before the court, we are pleased to see that the tools we have in place to detect wrongdoing, including giving staff the channels and power to speak up, are working and enabled this to be brought to our attention."