The YouGov poll, commissioned by the People’s Vote campaign calling for a public vote on Brexit negotiations outcome, found 48 per cent of respondents were in favour, with 31 per cent opposed.
This is greater than the UK wide-response of 45 per cent for and 34 per cent against.
Researchers surveyed 2,013 adults in Scotland between August 8 and 14 and found rising support for staying in the European Union.
Two-thirds (66 per cent) said they wanted to remain while 34 per cent were pro-Brexit, when the don’t knows were removed, while in the 2016 referendum voters in Scotland were split 62 per cent to 38 per cent for remain over leave.
The poll reveals around one in 10 Scots (12 per cent) believes Britain will get a good Brexit deal.
Most believe Brexit will make Scotland’s economy weaker at - 56 per cent to 12 per cent - and their standard of living worse at, 49 per cent to 7 per cent.
A majority of Scottish voters (65 per cent) believe the UK Government is ignoring Scotland’s concerns on Brexit, while 16 per cent believe it is listening.
There is a high level of distrust about the UK Government taking the right decisions on Brexit, with 70 per cent distrustful and 21 per cent the opposite.
In comparison, 48 per cent said they do not trust the Scottish Government to take the right Brexit decisions, while 42 per cent did.
The poll also indicated widespread support among SNP, Labour and Liberal Democrat voters for staying in the EU and at 73 per cent, 67 per cent, and 77 per cent respectively.
Conservative voters were 29 per cent in favour of staying in the EU with 64 per cent backing Brexit.
SNP voters back a Brexit deal referendum by a margin of more than four to one, 66 per cent to 18 per cent, when the don’t knows have been removed while for Labour this is 74 per cent to 26 per cent.
On Scottish independence, 43 per cent of respondents said Brexit would make this more likely and 6 per cent said it would be less likely.
More than a quarter (28 per cent) said it would make no difference as independence has little or no chance anyway, while 7 per cent believe Brexit would make no difference as Scotland gaining independence is likely regardless.
Former YouGov president Peter Kellner said the poll shows public opinion on Brexit shifting.
He said: “Support for a public vote on the outcome is growing across the UK but is particularly strong in Scotland where most people did not want to leave in the first place.
“There is deep pessimism about what Brexit will mean for Scotland and the next generation. Around two-thirds of Scots think the UK is ignoring their concerns and don’t trust Westminster to take these decisions.
“But the survey suggests the leaderships of both the SNP and the Labour Party are in the wrong place with most of their supporters.
“There may be an electoral dividend in Scotland for one of these parties if they strengthen their position.
“For instance, by a margin of three to one Labour supporters want Jeremy Corbyn to campaign for a public vote while Nicola Sturgeon may yet want to move faster than she has in backing such a route on Brexit.”
The campaign group has organised a rally in Edinburgh on Saturday calling for a referendum on the Brexit deal.