The majority of people (85%) believe it would make no difference to their holiday choice if the country votes to leave the UK in September.
Of those who said it would make a difference, about half would "want to visit even more". About 8%, mostly from the South of England, said they may avoid travelling to Scotland.
Younger people were most likely to say independence would make them more inclined to visit.
The most positive impact would be in the Republic of Ireland, where about 11% of respondents said independence would make them want to visit even more.
People in the North of England appear to have a closer affinity with Scotland than those in the south of the country, the survey suggests.
The Dunira Strategy survey into Scotland's most important industry is based on responses from 1,834 people, interviewed between February 18 and March 7.
Managing director Benjamin Carey said: "A number of commentators have argued that independence could jeopardise growth in the UK staycation market, which is a key component in the recovery of Scottish tourism following the economic crisis.
"This survey shows that these fears are unfounded. Certainly VisitScotland would need to work hard to engage the South of England, but there are also opportunities to reward the loyalty of the North of England and the Celtic affinity of the island of Ireland.
"With Scotland already punching above its weight internationally, a renewed focus on tourism from the British Isles will ensure that Scotland is building on its outstanding credentials as one of the world's strongest tourism brands."
A spokesman for Tourism Minister Fergus Ewing said: "Scotland is a fantastic place to visit, and we look forward to welcoming tourists from all over the world during this second Year of Homecoming.
"We welcome these findings which show that an independent Scotland will continue to be a hugely attractive destination for people from all over the UK and Ireland.
"Scotland is in the global spotlight as never before, and securing our status as an independent country will only add to our international profile and help to attract visitors from all over the globe."