The answer is "yes, but," according to the information Judith Evans Grubbs presents in Women and the Law in the Roman Empire: A Sourcebook on Marriage, Divorce and Widowhood.
As a child, a woman was subject to the power or potestas of her father, the paterfamilias. Upon marriage, she might be handed over formally to the hand or manum of her husband, at which time all property she had or would acquire became the property of the paterfamilias of the family into which she had married. (If she weren't married in manu, she remained under her own father's potestas.) The paterfamilias into which the woman married would usually be either her husband or his father. If her husband died, the Roman matron came into her own power: She was said to be sui iuris. Being sui iuris meant the Roman matron could own property.
Because by the end of the Republic, in manu marriages had become infrequent, Augustus changed the laws slightly, making it a little easier for a woman to be sui iuris. Specifically, Augustus changed the person who had to die. Now it had to be the Roman woman's own father or paterfamilias, who, since he was presumably older than her husband, could be expected to die sooner than her husband.
In the case of a man divorcing his wife, the dowry might go to the wife, her paterfamilias, or be divided, with part of it staying with the ex-husband. The wife's paterfamilias would take repossession of the dowry -- if he were still alive. If the paterfamilias were not still alive, the dowry would go to the wife. There were two main exceptions. If the husband instigated divorce proceedings because of his wife's wrongdoing or if there were children, he might keep part of the dowry.
Judith Evans Grubbs says that from an early period in Rome, women not married in manu had the right to divorce. Sometimes the wife's father might instigate the return of the dowry -- divorce -- on his daughter's behalf. In these cases, also, the husband might lay claim to part of the dowry.