The survey commissioned by the Sky News broadcaster also found that the 46% of the 590 people polled between September 2-8 said they would support holding another independent referendum in the next five years, while 44% were against it.
Scots voted to remain in the United Kingdom in a 2014 referendum but that support shrunk after a majority of the UK chose to leave the European Union two years later. Scotland voted to remain in the European Union in the 2016 referendum, but the overall UK vote was to leave.
UK Prime Minister Boris Johnson has repeatedly said that another vote on Scottish independence would be "irresponsible" and "reckless," but his cabinet minister, Michael Gove, said on 1 August that the UK government would let Scotland hold a second independence referendum if there was a "settled will" of the public.
Later in August, the secretary of state for Scotland, Alister Jack, suggested that a 60% support for independence would be needed to trigger another referendum.