Public health experts in Edinburgh have recommended the tariff in a new paper examining how to tackle the nation's weight problem.
The "sugar tax" levy on soft drinks and fruit juices would be equivalent to a 6p increase in the price of a can of Coca Cola or Irn-Bru and a 10p hike in the cost of a small bottle.
Family-sized two-litre bottles of the beverages would cost 20p more than they are now.
Sugar-free juices and diet versions of the drinks would not be affected.
The measure is outlined in the paper Policy Interventions to Tackle the Obesogenic Environment, which was produced by researchers at think-tank the Scottish Collaboration for Public Health Research and Policy (SCPHRP).
The work was commissioned by the NHS and funded by the Scottish Government's Chief Scientist Office.
John Mooney, a public health specialist for SCPHRP who led the work, said such a tax would impact on consumption rates among young people in particular.
He said: "This is something the Scottish Government can't afford not to look at. We have to tackle the enviromental factors that lead to obesity.
"A tax targets those who are most likely to consume the most fizzy drinks. Teenagers in particular are hard hit by the move."
Similar taxes have already been introduced in countries including the United States and France.
Other European countries, including Denmark and Hungary, have also introduced a "fat tax" on junk food and other fattening foods.
A tax on sugary drinks would follow on from the Scottish Government's minimum price-per-unit on alcoholic drinks to cut alcohol-related violence and illness in Scotland.
The main aim is to encourage people to opt for a sugar-free or diet beverage as an alternative to their usual high-calorie drink. The report has now been passed to the Scottish Government.
Scots are well-known for having a sweet tooth, which has contributed over the years to wider waistlines as well as poorer dental health among Scots compared to their counterparts elsewhere in the UK.
By the age of 15, one-third of boys and one in five girls are consuming sugary drinks daily.
There have been signs of improvement, with a recent report by the World Health Organisation finding the number of 11 to 15-year-old girls drinking fizzy drinks every day has halved over the last ten years. Consumption has also halved over the same period among 11 and 13-year-old boys.
A spokesman for the British Soft Drinks Association said: "This is not the way to fight obesity. All foods and drinks have a place in a sensible, balanced diet."
Scottish Conservative health spokesman Jackson Carlaw, said: "The SNP should realise that measures such as this 'Irn Bru tax' would make the country thoroughly miserable."
Professor Mike Lean, chairman of Human Nutrition at Glasgow University, said: "It would be a good idea to consider this. There has been indecision and pandering to industry for far too long."
A Scottish Government spokesman said: "This report explores taxation, but makes clear the views are those of the researchers and not the Scottish Government."
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