Ian Taylor is the biggest single donor to the Better Together group led by former Labour Chancellor Alistair Darling.
The businessman, who is also said to have given more than £500,000 to the Tories and become embroiled in a "cash for access" scheme involving dining at Downing Street, put up half of the £1.1 million raised for the campaign for a No vote.
In addition to involvement in the controversies, Mr Taylor's Vitol international trading group also avoided UK tax. He is its president and chief executive.
SNP Westminster leader Angus Robertson said the onus was on Mr Darling to launch a probe. He said: "Material in the public domain states that during his tenure as chief executive Mr Taylor's company paid £1m to Serbian war criminal Arkan, who was indicted at The Hague for crimes against humanity.
"During his tenure it is reported Vitol pleaded guilty to paying surcharges to Iraq's national oil company during Saddam Hussein's regime, undermining the UN oil-for-food programme in Iraq, and was involved in a tax avoidance scheme in the UK for over a decade.
"Mr Taylor's donations to the Tory Party were questioned and criticised by Labour's Douglas Alexander in relation to a conflict of interest about oil contracts in Libya, so the campaign must have been aware of these matters.
"We know Alistair Darling met Mr Taylor to discuss his donation. We need to know if he asked him about any of these issues.
"The No campaign must hand this money back until Mr Darling has been able to answer."
Better Together said: "Allegations were made about one of our donors in a Nationalist blog a few days ago. These were only covered in the press after a fresh and cynical attack by Angus Robertson as they desperately tried to create a story.
"We understand the claims are now being dealt with by lawyers representing Ian Taylor. As such we are limited in what we can say on this. However, they have made it clear to the media that the reports are inaccurate.
"What we are happy to say is Ian Taylor is a respected figure internationally, in the UK and in Scotland. He has a long history of philanthropy and his personal investment has revived the Harris Tweed industry in Scotland."
Vitol addressed reports in 2001 that the firm paid £1m to Arkan to put back on track an oil deal with the regime of Slobodan Milosevic which had turned sour. It said the move did not involve any illegal conduct on its part. It said: "At no stage has any government or regulatory agency investigated or accused Vitol of engaging in any illegal conduct in relation to the facts in question."
A statement said: "Vitol has acknowledged some payments were made outside the scope of the UN oil-for-food programme to the account of the national Iraqi oil company for the development of Iraq's oil infrastructure. These payments were surcharges demanded by the state oil company of Iraq. They were neither bribes nor kickbacks."
It also commented on an admission last year that it was involved in buying and selling Iranian oil in a deal with China. The company's Swiss status meant it did not technically breach any EU or US sanctions.
The company said: "Vitol has at no stage broken any sanctions on trading oil. Vitol is fully compliant with applicable international laws and regulations governing trade with Iran."
The firm would not comment on its tax affairs, after last year it emerged it had been using Employee Benefit Trusts.
It said it is satisfied all its tax affairs are compliant with the appropriate legislation.