The finding came in an opinion poll conducted by YouGov and commissioned by the SNP.
The cash from Vitol chief executive Ian Taylor to the unionist grouping was a personal donation.
But critics have called for it to be handed back because of Vitol's links to Serbia, Iran, Iraq and Libya amid reports it paid $1m (£660,000) to Serbian warlord Arkan to facilitate a deal.
The SNP said Better Together leader Alistair Darling would be wise to take heed of the poll's findings.
But Better Together accused the nationalists of "desperate" attempts to "divert attention from their hapless campaign".
The YouGov poll questioned 1006 adults in Scotland between May 1 and May 3.
Those surveyed were told: "Mr Taylor is the chief executive of the oil trading firm Vitol which has previously been fined after admitting making payments to the national oil company in Iraq during the regime of Saddam Hussein, and are reported to have paid $1 million to the Serbian paramilitary Arkan as part of an oil deal in the 1990s. Vitol are also in discussion with HMRC over links to tax avoidance schemes in the UK. The company said it has not acted illegally.
"There has been no suggestion that the donation is illegal or has broken any rules and the donation has been given by Mr Taylor in a personal capacity." They were asked: "Do you believe that the No campaign should or should not return this donation?"
Of those polled, 43% said that Better Together should hand the money back, 34% said that they should not and 23% said they did not know.
Among those who did have an opinion 56% backed the donation being returned while 44% supported keeping it.
SNP Westminster leader Angus Robertson MP said: "The reputational damage this is causing the No campaign is outweighing the value of the money."
A spokesman for Better Together said: "The Nationalists' desperate attempts to find something to divert attention from their hapless campaign shows no sign of abating.
"Ian Taylor has made a huge contribution to Scotland, including to charities endorsed by ministers. The SNP don't care about this, it would seem."
Vitol has said in response to reports of the $1 million payement that it did nothing illegal, and that it was is confident its tax affairs were compliant with the law.
l Deputy First Minister Nicola Sturgeon, Culture Secretary Fiona Hyslop and former minister Bruce Crawford are among 20 SNP MSPs who backed a Scots charity which took money from Mr Taylor.
The Taylor Family Foundation charity he founded has given millions to good causes, including several in Scotland. In 2009 and 2010 it gave a total of £50,000 to Sistema Scotland, the Stirling charity which teaches music to children in disadvantaged areas such as Raploch.
In September 2010, Stirling MSP Bruce Crawford, then SNP minister for parliamentary business, hosted a reception for Sistema Scotland at the Scottish Parliament.
Last November, the Scottish Government also gave Sistema Scotland £1.3 million to set up a "Big Noise" orchestra in Govanhill, which is in Ms Sturgeon's Glasgow Southside constituency.
Ms Sturgeon and Ms Hyslop took part in a photo opportunity to publicise the grant. Twenty SNP MSPs have also signed Holyrood motions supporting Sistema and its work.