The nationalists are ahead of Labour by 12 percentage points, with 41% of the vote, compared with 29%, according to the survey conducted by ICM Research.
The Scottish Conservatives are in third place with 13%, Ukip have 6%, while the LibDems trail on 5%.
Those surveyed were asked which party they thought they would vote for in the May 22 ballot.
The 1000 people polled were asked how they would vote in a referendum on the UK's EU membership if there was ballot tomorrow. Results show 47% of people would opt to stay in, while 30% would vote to leave. The remainder did not know.