The call to the Scottish Government is being led by Edinburgh golfer Simon Norris, who received nearly 100 signatures within a few hours of the petition going live on change.org.
"I am a keen golfer in Scotland and would like to be able to get back to playing soon," he told the Edinburgh Evening News/The Scotsman.
"Golf is an outdoor game which is played in large open spaces and can be played while easily adhering to social distancing rules.
"There are well-documented benefits from playing golf for physical and mental health, for all ages and genders. And of course, golf in Scotland is 'every person's' sport."
Norris, a member at Ratho Park, has included the Scottish Government, Scottish Golf, Active Scotland and sportscotland on a list for his petition.
"I am frustrated at the speed of the government allowing golfers back onto their courses during this lockdown period," he added.
"There are discussions going on between the Scottish Government, Department of Public Health, Sport and Wellbeing, Scottish Golf, Active Scotland and sportscotland. I feel there is a great deal of discussion between these bodies, but no one is asking ordinary golfers their opinion.
"That prompted me to start his petition - change.org/PlayGolfAgain. While I understand that there are many urgent public health issues to do with coronavirus which are close to everyone's lives, this felt like a small but positive step we could make very simply and quickly."
The R&A has submitted proposals for "safe golf" when courses reopen to the UK Government, raising hopes that the green light could be given in the next week or so.
It has been reported that clubs in Wales were preparing to reopen as early as next week with the strict measures in place.
"I am aware that the Scottish Government are considering 'small incremental steps initially in terms of easing the measures' as part of their COVID exit policy," said Norris.
"I would like to recommend that we consider allowing people to play golf again, now.
"There are well-documented health benefits that golf provides participants both physically and mentally.
"Golf is played in quiet wide open spaces and is enjoyed by people of all ages. It is possible to play golf while respecting the two metres social distancing guidance, but allowing some element of social contact with playing partners. And most players have only a short journey to their course.
"Scotland has over 188,000 players and nearly 600 courses, so allowing people to play would benefit many people, without endangering others or the Government's COVID strategy."
A message from the Editor:
Thank you for reading this story on our website. While I have your attention, I also have an important request to make of you.
With the coronavirus lockdown having a major impact on many of our advertisers - and consequently the revenue we receive - we are more reliant than ever on you taking out a digital subscription.
Subscribe to scotsman.com and enjoy unlimited access to Scottish news and information online and on our app. With a digital subscription, you can read more than 5 articles, see fewer ads, enjoy faster load times, and get access to exclusive newsletters and content. Visit https://www.scotsman.com/subscriptions now to sign up.
Our journalism costs money and we rely on advertising, print and digital revenues to help to support them. By supporting us, we are able to support you in providing trusted, fact-checked content for this website.