The SNP-commissioned survey found support for independence tied with support for the Union at 50 per cent as the Nationalists prepare for their national conference in Glasgow.
A majority of the respondents polled by Survation - 52% - also said they would vote Yes if the UK left the EU with no deal.
First Minister Nicola Sturgeon said: “Support for Scotland becoming an independent country is at historically high levels - above the hugely impressive result secured in the 2014 referendum.
“It also shows that regardless of the type of Brexit the Tories offer, the simple fact of Brexit will increase support for independence to 50%.
A second poll found almost nine out of ten SNP members back a so-called “People’s Vote” on the final Brexit deal.
A YouGov poll of 665 SNP members ahead of today’s party conference in Glasgow found that 89 per cent supported a referendum on the withdrawal deal negotiated by Theresa May with the EU.
The survey found a margin of 89 per cent to 11 per cent in favour of another vote when “don’t knows” were excluded.
The research also found that a convincing majority (79 per cent) believed that SNP MPs should support a People’s Vote if faced with an amendment to Brexit legislation that would facilitate another referendum. Just 8 per cent said MPs should oppose it while 13 per cent believed they should abstain.
The research comes as the SNP’s Westminster leader, Ian Blackford, said the party would support a second referendum on Brexit – but only if it could hold another vote on independence.
Such a re-run of the vote on Europe would also depend on a clear assurance that if most Scots chose to remain in the EU, but the opposite happened in the rest of the UK, then Scotland would not be forced to accept the result.
“We have to have the protection of knowing that if the UK has a second vote and we end up in the same situation as we had in 2016, we would be able to determine our own future,” he said.
The YouGov poll showed no fewer than 98 per cent of SNP members believe Theresa May’s government is ignoring Scotland’s concerns about Brexit and 93 per cent believe the UK will not get a good deal.
A spokesperson for the People’s Vote campaign said: “There is growing support in every part of the UK to give voters the democratic opportunity to cancel Brexit, and the SNP and people of Scotland have a crucial role to play in cleaning up a mess that is not of their making.”
Stephen Gethins, MP, the SNP’s foreign affairs and Europe spokesperson, said: “This polls reveals that SNP members see straight through the Tories’ false claims on Brexit, and hold absolutely no faith in the Tory government being able to deliver.”