A majority of SNP councillors banded together with some Liberal Democrat, Green, independent and Labour members to defeat the ruling Tory administration.
The council voted by 33 to 26 in favour of a motion by Green councillor Martin Ford to back a so-called People’s vote.
Now, the Scottish Conservatives have accused the SNP of “betrayal” after some nationalists backed the move for a vote on the Brexit deal terms.
The symbolic council decision - the first of its kind in Scotland - puts the SNP councillors who voted in favour at odds with their party position on a People’s vote.
First Minister Nicola Sturgeon has said she will not stand in the way of a People’s vote but has not backed the campaign, raising concerns over the possibility of Scotland again voting to remain but the UK as a whole voting to leave.
However, Constitutional Relations Secretary Mike Russell told MSPs he has had “very constructive” talks with the People’s vote campaigner Hugo Dixon.
Tory MP David Duguid, who represents the Aberdeenshire constituency of Banff and Buchan, said he was “astonished” some SNP councillors representing fishing communities backed the People’s vote.
He said: “The British people - including those here in Banff and Buchan - voted to leave the EU.
“People voted to leave for a number of different reasons. But in coastal communities like those across Banff and Buchan, many people just wanted out of the Common Fisheries Policy.
“Failure to respect the outcome of the vote would be an utter betrayal of our fishermen and a travesty for democracy in this country.
“The question for Nicola Sturgeon is - does she agree with her SNP councillors in Aberdeenshire and is she also willing to disregard the views of our fishermen?”
SNP opposition leader on Aberdeenshire Council Richard Thomson said: “The SNP moved an amendment recognising the severe damage that Brexit will have upon Aberdeenshire – something which the Tories seem to be recklessly ignoring. That damage will be acutely felt by key North East industries such as our food and drink and oil and gas sectors.
“When jobs are lost, the Tories will be to blame. When exports of Scottish seafood face lengthy delays at the border, the Tories will be to blame. “And when our fishing fleet is sold out as part of a Brexit trade-off, the Tories will be to blame.
“It is simply a fact that to protect jobs and household incomes after Brexit we must remain in the single market and customs union, which is eight times bigger than the UK market alone. The SNP will continue to make that case.
“Meanwhile, we’ll leave the Tories to act as cheerleaders for Theresa May’s botched negotiations, as they ignore the will of people in Aberdeenshire and across Scotland who voted to Remain in the EU.”