A Survation poll for the eu+me group found 63.37% of people in Scotland agreed on having the ability to make different choices to the rest of the UK.
Nearly a fifth (19.97%) disagreed, 12.92% neither agreed nor disagreed and 3.75% said they did not know.
But when removing the “don’t knows” and no preferences, 83% agreed while 17% disagreed.
Its Scottish poll of 1127 people took place between June 9 and 16.
There was similar support from a UK-wide poll of 1022 people on June 9 and 10.
Nearly half (44%) of the UK survey respondents agreed on Scotland setting its own immigration policy with 29% disagreeing.
A quarter (24%) neither agreed nor disagreed while 3% did not know.
After removing these figures, the results were 61% agreed and 39% disagreed.
Earlier this month, the Scottish Government’s independent expert advisory group on migration and population suggested immigration into Scotland could be halved by the proposed salary threshold and risk staff shortages in areas such as the care sector.
Home Office plans post-Brexit would require migrant workers to earn at least £25,600 a year to be able to work in the UK.
Fergus Mutch, eu+me director, said: “With just five months remaining until free movement comes to an end, there’s real trepidation about what comes next and how we replace a system which has helped all EU nations to grow and flourish in recent decades.
“We want European citizens to come here to live, work, study, enrich our communities and help our country prosper for many years to come.
“There’s an increasing sense of frustration that this UK Government’s immigration approach is not working for Scotland and risks doing a great deal of damage – the consequences of which could be permanent.”
He added: “That’s why more and more people believe we must have a tailored system which works in Scotland’s interests.
“And across the UK, there’s little resistance to Scotland having control of those powers.
“It’s the popular policy, the common sense policy and the right policy.
“With the power to set our own course on immigration we can maintain alignment with the EU 27, keep the door open to the exchange of talent and expertise from Europe and, ultimately, make the process easier to be back in the EU before long.”
The Home Office is yet to comment