BUCHAREST, Romania — Viorica Dancila was approved by the Romanian Parliament as prime minister on Monday, becoming the first woman to hold the position in the country’s history despite doubts about her relative lack of experience and the continued influence of a party leader who has been convicted of vote fraud.

Ms. Dancila, 54, a member of the European Parliament since 2009, will take power after her cabinet was approved by Parliament, 282 to 136. She is the third prime minister in a turbulent 12 months for the country that has included a wave of anti-government protests, the largest in a quarter-century, over legislation that would have eased the penalties for corruption.

Ms. Dancila was formerly a little-known politician, and her low profile, some of the cabinet choices, and her ties to Liviu Dragnea, the powerful leader of the governing Social Democrat Party, mean that she will enter office with many Romanians skeptical of her independence and her ability to bring stability and usher in a more progressive era, especially as the country wrestles with corruption and growing disillusionment with the political class.

Mr. Dragnea was unable to become prime minister because of a conviction for electoral fraud, and is also under investigation for misuse of state money, including European Union funds.