The majority of fans would also like safe standing areas to be introduced in grounds and supporters represented at board level at their clubs.
The Supporters Direct Scotland National Football Survey of almost 3,000 fans found almost 62 per cent were in favour of lifting the alcohol ban.
However the majority of women (51.5%) who responded were against ending the restriction.
Drink was banned at football games following rioting during the Scottish Cup final in 1980.
When asked if they thought the ban had been successful in reducing crowd disorder, almost half (48.28%) of participants thought it had. Nearly three quarters (72.4%) were in favour of the introduction of a small scale trial.
The study found nearly 91% of participants were in favour of seeing safe-standing areas being introduced.
Of those who do not attend games regularly, almost half (48.79%) claimed they would be more likely to go to matches if they had the choice to stand.
Paul Goodwin, head of Supporters Direct in Scotland, said: "It is important for every business to understand what its customer base wants and football is no different. The Scottish FA recognises this and their increased support for the work we do is welcomed."