The Survation survey shows 61% think the Scottish, Welsh and Northern Irish governments should be heard at the talks.
Just under a third (32%) do not want the devolved administrations to have a place in negotiations, while 7% do not know.
The poll also shows almost half of respondents (49%) lack confidence in the UK Government’s ability to secure a good Brexit deal, while 38% are confident and 13% do not know.
Researchers surveyed 1,017 adults across Britain between June 28 and 30.
First Minister Nicola Sturgeon has repeatedly called for Scotland to have a seat at the table in Brexit negotiations.
In her Article 50 letter triggering the start of the Brexit process Theresa May said the interests of the nations and regions of the UK would be taken into consideration, but she stressed that during the talks ‘’we will negotiate as one United Kingdom’’.
An SNP spokesman said: “This shows clear backing from people across Scotland, by a margin of almost two to one, for the Scottish Government’s call for the devolved administrations to have a seat at the Brexit negotiating table. That simply reflects the growing momentum and consensus, including backing from business chiefs, that Scotland should have a place at the talks.
“But this poll also shows people have no confidence that Theresa May can get a good deal - and that reflects the Tories’ reckless threat to walk away with no deal at all, which would be catastrophic for jobs, investment and living standards.”