Nearly half of all voters surveyed also said they would vote for the UK to remain in the EU if asked tomorrow.
David Cameron has promised an in-out referendum on EU membership in 2017 if the Conservatives win the next General Election.
EU membership has been a central plank of Alex Salmond’s drive to convince Scottish voters of the benefits of independence.
European Commission president Jose Manuel Barroso said earlier this week that admission to the EU for Scotland would be “extremely difficult, if not impossible” - but his comments were criticised by former EC Director General Jim Currie as “unwise and incorrect”.
In a poll carried out by the Daily Mail surveying 1,005 people 16 and over, 48.7 per cent said they were in favour of the UK staying in the EU, while 35.4 per cent said the UK should leave.
Asked if an independent Scotland should host a referendum on EU membership, 63.4 per cent of respondents agreed.
A spokesman for Survation, the company who carried out the poll, said: “In comparison with Yes voters, No voters are significantly more likely to be in favour of staying in the EU. This would suggst that fear of not being in the EU could be a factor in motivating some people to vote No to an independent Scotland.”
Deputy First Minister Nicola Sturgeon said: “This poll shows strong support for remaining in the European Union, at 58 per cent when ‘don’t knows’ are excluded. The danger of a No vote in September is that we could be dragged out of Europe against our will by the in-out referendum that David Cameron plans for 2017.
“We believe that Scotland’s future is as an independent nation in the European Union.”