Young people aged 11 to 15 are picking up the habit at a rate of 19,900 each year, figures released by Cancer Research UK show.
The charity has called on the Scottish Government to act quickly on its pledge to introduce legislation on plain packaging for cigarettes. A similar move by the UK Government was put on hold earlier this year.
Research shows that packaging without branding is less appealing to children, the charity said.
Its Setting the Standard campaign promotes action to discourage young people from starting to smoke.
Vicky Crichtonhe, the charity’s senior public affairs manager in Scotland, said: “Smoking is a serious problem in Scotland with almost 20,000 children, tempted by glitzy, slickly designed packs, being lured into starting smoking every year. It is an addiction that is often life-long and kills more than 4,000 Scots annually.
“If the Scottish Government is serious about curbing the death toll caused by this lethal habit and meeting its goal for Scotland to become a nation free from tobacco by 2034, then swift action needs to be taken.
“We urge MSPs to shun the myths perpetuated by the tobacco industry and commit to a firm timetable to bring in this important, life saving legislation.”
Evidence from Australia, where plain cigarette packaging was introduced in December last year, appears to show smokers finding cigarettes less appealing, Ms Crichtonhe said.
A Scottish Government spokeswoman said: “The Scottish Government is committed to introduce standardised packaging, based on the strong evidence to support the impact it will have on preventing young people from starting to smoke. We will identify an appropriate timescale to introduce legislation on standardised packaging to the Scottish Parliament.
“Our recently launched Tobacco Control Strategy, Creating a Tobacco Free Generation lays out a range of key measures aimed at preventing young people from starting to smoke.
“As well as the introduction of standardised packaging and the implementation of the display and vending machine bans which will address the attractiveness and availability of tobacco, other key actions include establishing a Youth Commission on Smoking Prevention and piloting of the schools-based ASSIST programme.”
The latest figures were based on rates in the Survey of Smoking, Drinking and Drug Use among Young People in England carried out by the NHS Information Centre for Health and Social Care.
Statisticians at Cancer Research UK produced figures for Scotland and the rest of the UK, based on 2011 population estimates.
Eight out of ten adult smokers start the habit by the age of 19 and more than a quarter (27%) of all under 16s - the equivalent of one million children across the UK - have tried smoking at least once, according to the charity.