The latest survey by Panelbase put support for leaving the UK at 52 per cent, with 48 per cent backing the union. The study was carried out on January 28-31 on behalf of the Scot Goes Pop blog.
The results come a day after another poll by Survation on voting intention found both the “yes” and “no” camps on 50 per cent each.
A week earlier a YouGov survey saw “yes” inch into a slight lead on 51 per cent, with many Remain voters in the EU referendum switching from “no” to back independence as a result of Brexit.
"Scotland has been dragged out of the EU against our will by a Tory government and prime minister that we didn't vote for, and who are undemocratically trying to block the people of Scotland having their say in a referendum. But that position is unsustainable — ultimately the people of Scotland will have the chance to escape Boris Johnson's Brexit Britain and choose a better future as an independent European nation.
"The case for independence grows stronger by the day. The longer Boris Johnson tries to ignore the SNP's democratic mandate, the more support for independence will continue to grow."
Sir John Curtice, professor of politics at Strathclyde University, told the pro-independence newspaper: "Now that Brexit has happened it looks as though a few more Remain voters have switched sides — adding to the evidence that the pursuit of Brexit is serving to undermine the foundations of support for union.
"At present, at least, unionists are clearly on the back foot in the constitutional debate north of the border." Scotland in Union, the unionist campaign group, said it was a reminder that support for the union could not be taken for granted. Pamela Nash, the chief executive, said: "We know the overwhelming majority of people in Scotland don't want a divisive second independence referendum this year, but Nicola Sturgeon is ramping up her campaign in a desperate bid to deflect from the SNP's failings in office.
"She should stop trying to divide Scotland and focus on fixing the public services her government has run into the ground. Scotland deserves better."
Boris Johnson has refused to transfer the power to hold a legally binding referendum to the Scottish parliament.