The study found that heavy smoking was linked to offending regardless of whether the child was brought up in socially deprived circumstances.
The researchers from the Harvard School of Public Health in the US found an increased risk for women who smoked 20 or more cigarettes a day during pregnancy.
Experts said smoking during pregnancy was already linked to a range of health problems, with the latest study adding to reasons for women to quit.
The new study enrolled more than 3,700 mothers between 1959 and 1966 and asked about their smoking habits during pregnancy.
In 1999-2000, when their children were aged at least 33, criminal record checks were carried out on the offspring.
The results showed that those children whose mothers smoked heavily were 31 per cent more likely to have been arrested as those whose mothers never smoked, and were more likely to be repeat criminal offenders.
The researchers said: "The offspring of mothers who smoked heavily during pregnancy had a 47 per cent increased odds of multiple (arrests) versus no arrests." The findings were the same for both men and women.
The team concluded: "While we cannot definitively conclude that maternal smoking during pregnancy (particularly heavy smoking) is a causal risk factor for adult criminal offending, the current findings do support a modest causal relationship."
The researchers said some biological evidence suggested that nicotine would have an impact on the developing brain influencing behaviour.
Other work has suggested a link between exposure to cigarette smoke in the womb and a higher risk of poor attention span, impulsivity and hyperactivity.
Professor Kate Pickett, from the department of health sciences at the University of York, said: "This study adds to a substantial body of evidence linking smoking in pregnancy to difficult temperament in infants, behaviour problems in children, and antisocial behaviour in adult offspring.
"These relationships seem to be robust, and can be seen even after accounting for many differences between women who smoke and those who manage to quit, or never smoke in pregnancy.
"However, we also know that smoking in pregnancy is related to multiple and complex challenges faced by women in their own lives, in their family circumstances and in the neighbourhoods in which they raise their families.Women need interventions and encouragement to help them quit smoking, but they also need joined-up services and support to help them be the best parents they can."
Dr Ron Gray, from the National Perinatal Epidemiology Unit at the University of Oxford, said: "Whether or not mothers' smoking during pregnancy causes criminal offending in their children - and this well-conducted study strongly suggests that it might - there is abundant evidence that it causes stillbirth, low birth weight and infant death, as well as damaging the mothers' own health."