"It has happened six or seven times and it's always an unknown number. It is usually after stuff has been posted on one of the main smokers' websites.
"They don't leave their name, they just say things like 'Keep taking the money', and 'Who are you to try to intervene in other peoples' lives', using a couple of profanities."
Bauld has not reported the calls to the police but intends to be more discreet about the availability of her telephone number.
There is no evidence that tobacco companies are directly responsible for the anonymous phone calls.
But Bauld has been identified as a legitimate target for criticism by Big Tobacco after her high-profile work on cigarettes and the effect of smoking bans.
Her report for the Department of Health last March on the smoking ban in England found that there had been positive benefits to health and no evidence of any obvious negative effect on the hospitality industry, as the tobacco industry has repeatedly claimed.
Imperial Tobacco, the biggest cigarette company in Britain, responded to Bauld's report with its own review, called The Bauld Truth.
This report, which took only a few weeks to produce, claimed that Bauld's study, conducted over three years, was "lazy and deliberately selective".
It claimed she used flawed evidence and did not validate her findings.
Bauld said such personalised attacks were nothing new.
Big Tobacco had a long history of aggressively dismissing scientific evidence linking smoking to ill health, she said.
She said such studies were heavily peer-reviewed at every stage.
"Their methods are robust, whereas the evidence [the tobacco companies] draw on are not well-conducted studies."
- Independent