Drinking one drink every day for 10 years, or two drinks a day for five years, raises the risk by 5 percent.
One drink contains 23 grams of ethanol, which is the equivalent of a bottle of beer, a six-ounce glass of wine, or two ounces of whisky.
Although the amount we drink is a factor, the risk is more linked to the frequency of drinking, and so the antidote is to drink less often or not at all, researchers at the University of Tokyo report.
They have taken a special interest in the causes of cancer because it is the biggest killer in Japan and is far more lethal than heart disease, which remains the deadliest in the West.
They analysed clinical data from 63,232 cancer patients and compared them to a similar number of healthy controls. Both groups reported on the amount and frequency of the alcohol they drank.
The researchers discovered a linear connection between alcohol drinking and cancer, and especially the cancers most commonly linked to drinking, such as colorectum, stomach, breast, prostate and oesophagus. In other words, the more the participants drank, the more likely they were to develop cancer.