Cancer Research UK, which carried out the poll, said the findings showed a "shocking" level of ignorance on the subject – despite the fact one-quarter of people north of the Border are smokers.
When asked to name cancers linked to smoking, more than six in 10 Scots interviewed knew it caused cancers of the lung, mouth (oral) and throat (larynx and oesophagus). But fewer than 25% knew tobacco was linked to leukaemia and cancers of the liver, pancreas, bowel (colorectum), kidney, bladder, cervix and ovary.
Only 36% of the 239 people questioned for the study knew stomach cancer was linked to smoking.
The charity released the results eight days before the end of a UK-wide Government consultation on cigarette packets. It is calling for all tobacco products to be sold in plain packs without identification or branding, as research shows the striking logos and distinctive designs make them more appealing to children.
It is urging people to sign its petition against branding.
Linda Summerhayes, Cancer Research UK's spokeswoman for Scotland, said: "The list of cancers linked to smoking is truly striking. It's a long list of body parts that are affected, reflecting just how deadly tobacco is. Once a smoker is hooked it can be extremely difficult and take years to quit. The longer a person smokes, the greater the risk of illness.
"Eight out of 10 smokers start by the age of 19. The key to reducing the number of lives blighted by tobacco is to prevent young people from starting smoking in the first place. And reducing the appeal of cigarettes is vital to this goal.
"That's why we're urging people in Scotland to sign our petition and help protect children from a product that kills half of all its long-term users."
Robert West, professor of health psychology and director of tobacco studies at University College London, said: "Nearly everyone knows that smoking causes lung cancer. And smokers may often gamble with their chance of developing the disease. The addiction can lead people to reason that they might avoid lung cancer. But the odds aren't good. And these alarming results show what could be a fatal level of ignorance in Scotland about the toxic hit list from tobacco.
"There are only two options to eliminate illness caused by smoking: help smokers to quit and stop young people from starting to smoke."
Smoking is by far the most important preventable risk factor for cancer in the UK, and causes more than 28% of all deaths from the disease.
About 43,000 lives were lost to smoking-related cancers in the UK in 2009.
Meanwhile, the cancer charity Maggie's constructed a "pop-up" Maggie's Centre in the heart of Glasgow at the weekend.
The centre, at the St Enoch shopping centre, enabled people to experience first-hand the work of the charity.
Shoppers were able to speak one-to-one with Maggie's staff and volunteers for a unique insight into its vital work.
Glasgow's two Maggie's centres work in tandem to serve the west of Scotland – an area with a high incidence of cancer.
Gillian Hailstones, centre head for Gatehouse and Gartnavel Maggie's, said: "We take great pride in the work that we do to continue Maggie Jencks's vision for supporting people with cancer and those who care for them.
"The centres help people find their way through the confusion a cancer diagnosis can bring and encourages a sense of community through meeting others in similar situations."