This compares to only 22 per cent who said ministers should make control over immigration their number one aim, according to pollsters Ipsos MORI.
This is the fifth poll since the EU referendum to show people prioritising access to the single market over restricting freedom of movement.
The Scottish Government is demanding that access to the EU single market be maintained in the post-Brexit negotiations, although EU leaders have indicated this would mean that free movement of labour must be maintained.
Nationalist MSP Joan McAlpine, convenor of Holyrood’s European committee, said: “This poll shows that the Scottish Government is absolutely right to be exploring all possible options to keep Scotland in the EU with access to all the benefits that this brings – and this position is supported across Scotland.
“The European single market is vital to jobs, businesses and opportunities across Scotland and it is welcome news that people across the country share this view.”