A Panelbase survey of more than 1,000 people for The Sunday Times Scotland found that 30% said they support the measure, which has the backing of the Scottish Government.
More than half (53%) told pollsters they believe smacking should still be allowed, while 17% said they did not know.
Legislation aimed at banning smacking was published at Holyrood last month.
Green MSP John Finnie introduced the Children (Equal Protection from Assault) (Scotland) Bill after gaining the backing of Scottish ministers and MSPs from across all the political parties.
If passed, the legislation would remove the defence of “justifiable assault” in Scots law, which allows parents to use physical punishment to admonish a child.
Mr Finnie’s Member’s Bill is also supported by a range of organisations including the Scottish Police Federation, Barnardo’s Scotland, the Church and Society Council of the Church of Scotland and the NSPCC.
But the move is opposed by campaign group Be Reasonable Scotland - backed by The Christian Institute and The Family Education Trust - which argues a ban will “criminalise parents”.
A Be Reasonable spokesman said the Scottish Government is “out of touch” with the public on the issue.
He said: “The question for MSPs is not whether you should smack your children. It is whether you want to criminalise hundreds of thousands of parents who do.
“The clear evidence is that the vast majority of Scots do not back a ban. Those people need to communicate this to their MSPs before it’s too late.”
Responding to the poll, the Scottish Government pointed to findings from 2015 which it said showed that 92% of people say children should have the same protection or greater protection than adults from assault.
A spokeswoman said: “The Scottish Government supports positive parenting.
“This proposed Bill will give children the same legal protections as adults - something backed by an overwhelming majority of public opinion - and end the defence of ‘justifiable assault’.”
Panelbase surveyed 1,024 voters, the newspaper said.