But while 53% of the population support such a move, only 18% of smokers back it.
The findings were welcomed by anti-smoking campaign group ASH Scotland, which commissioned the poll, with chief executive Sheila Duffy insisting upping the taxes on tobacco is the "most effective way to cut tobacco use and save lives".
YouGov questioned 1064 people, with the results released on World No Tobacco Day.
Just over a fifth (21%) disagreed that taxes on tobacco should rise by 5% more than inflation every year.
The same proportion of ex-smokers were opposed to such tax rises, with 51% of those who have given up supporting the idea.
But among current smokers, 65% were against the idea of raising tobacco taxes by 5% more than inflation.
The poll asked how the UK Government could increase the amount of taxes raised to reduce its borrowings.
More than two thirds (69%) of people backed increasing the price of cigarettes to achieve this - the same amount of people who supported a "mansion tax" on properties worth more than £2 million.
The only proposal that was a more popular way for ministers to boost revenues was by raising the taxes on bank bonuses, which was supported by 74%.
Just over half (51%) want to see a tax on winnings from gambling, while 40% backed higher taxes on alcohol to help the Government cut its borrowing level.
Only 5% of people surveyed backed an increase in VAT to achieve this, while extending VAT to food was supported by 3%.
Ms Duffy said: "We are pleased that people in Scotland recognise the importance of increasing tobacco taxes. It is a measure that has a significant impact on public health and is highly cost-effective.
"Countries around the world have successfully increased tobacco taxes, decreased tobacco use and brought in significant new Government revenue."