And Two Fat Ladies at the Buttery is one of 11 eateries spearheading the campaign.
Zero Waste, Scotland's Good to Go initiative, aims to reduce the stigma of asking to take leftovers home after a meal out and make it more acceptable.
The organisation said research shows three-quarters of diners would like to see doggy bags offered in restaurants, but half are too embarrassed to ask for them.
It hopes the scheme will help reduce the tens of thousands of tonnes of food wasted each year when diners can't clear their plates in one sitting.
Iain Gulland, director of Zero Waste Scotland, said: "Over 53,000 tonnes of food is thrown away in restaurants in Scotland each year, which is not only a huge waste of money, it's also a huge waste of good food and the energy and water that went into producing it.
"Research shows that most people want to take leftovers home to enjoy later, but are embarrassed to ask, so the Good to Go pilot is all about making it a normal, mainstream thing to do."
The initiative is being piloted at 11 restaurants in Glasgow, Edinburgh, East Kilbride and Irvine.
Those participating include Two Fat Ladies at the Buttery, Cafe Gandolfi and Mother India in Glasgow and The Edinburgh Larder Bistro.
'Good to Go' branding will be on display in the restaurants to promote the availability of the take-home containers.
The scheme was launched at Two Fat Ladies at the Buttery, in Blythswood Street.
Its owner, Ryan James, chairman of the Glasgow Restaurant Association, said: "Especially in America, doggy bags are a huge part of the culture, mostly because the portions on the plate are too big to eat, so some of it goes in the doggy bag, but we noticed that here in the UK people are very reluctant to ask for one, and it's a case of are they reluctant to ask because they feel embarrassed to ask?
"What we're trying to do is break through that embarrassment barrier and encourage people to take their excess food home with them and reuse it."
He added: "As a restaurateur I'm obviously passionate about amazing food, so I'm delighted to support anything that helps to ensure as little as possible ends up needlessly going to waste."
The pilot will run until May 25 and research will be carried out to investigate the impact and determine if the scheme will be rolled out nationwide.
Environment Secretary Richard Lochhead said: "It's remarkable that the equivalent of one in six meals served in restaurants is thrown away. We want to reduce this, not only to make the most of the food we pay for when we're eating out, but also to help the environment."
Zero Waste Scotland, funded by the Scottish Government, works to maximise the effects of Scotland's natural resources, such as energy and water.