The Lord Ashcroft poll puts support for independence at 46% and 43% against.
The online poll questioned 1,019 adults in Scotland between July 30 and August 2.
It found 47% felt there should be a second independence referendum within the next two years, with 45% against the proposal.
First Minister said: “This is a phenomenal poll for the independence movement – showing that more and more people think it’s time that Scotland took our own decisions and shaped our own future as a fair, prosperous, outward-looking nation.”
Ms Sturgeon said the case for independence was growing stronger by the day as Scotland is "dragged towards a no-deal Brexit".
“It is time for us all to focus on what matters – growing our economy, and sorting out the mess the SNP is making of our education system and the NHS.”