It suggests that 47% will support independence if they believe they will be £500 a year better off, compared with just over a third who will oppose it (37%) and around one in six who do not know (16%).
In contrast, only one in five will back independence (18%) if they think they will be £500 a year worse off, compared with two in three who will support remaining part of the UK (66%) and around one in six do not know (15%).
Commissioned by The Scotsman and Scotland on Sunday newspapers, the ICM poll questioned 1,002 people between September 10 and 13.
It comes as the country approaches a year to go before the referendum next September.
Asked to consider how they will vote if they knew that the result of the referendum leaves them no better or worse off financially, 39% back independence, 44% oppose it and 17% do not know.
Around half say they think independence will be bad for the economy (48%), three in 10 think it will be good for the economy (31%), around one in 20 think there will be no difference (6%) and one in seven do not know (14%), according to the poll published at the weekend.
It also suggests that 49% of people would vote No, 32% would vote Yes and 19% do not know how they would vote on the referendum question: Should Scotland be an independent country?
Commenting on the poll, SNP deputy leader and Deputy First Minister Nicola Sturgeon said: "This is a welcome finding, underlining that people in Scotland know we've got what it takes to be an independent country.
"Scotland generates 9.9% of UK tax revenues and gets 9.3% of spending in return, and the most recent Government Expenditure and Revenue Scotland report showed that Scotland's finances are stronger than the UK's as a whole to the tune of £4.4 billion which equates to £824 per person.
"We are extremely confident, therefore, of demonstrating that we can build a more successful economy and fairer society with the powers of an independent Scotland."