By Steve Scherer

ROME (Reuters) - Virginia Raggi, the anti-establishment mayor of Rome elected by a landslide last year after pledging to crack down on rampant corruption, has been put under investigation for abuse of office and false testimony.

Raggi herself announced the investigation in a Facebook post on Tuesday. She will be questioned by prosecutors on Jan. 30, a judicial source said.

"Today I've received a subpoena from the Rome court," Raggi wrote, saying it was related to the nomination of the director of the city's tourism department, who was later removed from the position.

"I'm very serene and I have full confidence in the judiciary, as always," she wrote.

The news came just three weeks after the 5-Star Movement said it would not require its politicians who come under legal investigation to automatically step down.

Italy's largest opposition group presents itself as a squeaky-clean substitute to the tainted mainstream parties, which have been dogged by corruption for decades.

The June election victory of 38-year-old Raggi was meant to show the 5-Star Movement, which was founded by comic Beppe Grillo in 2009, was capable of managing a major city.

But almost from the start her administration was beset by resignations and infighting, and in December one of her aides, Raffaele Marra, was arrested on suspicion of corruption linked to a 2013 real estate deal.

Opinion polls nevertheless suggest that 5-Star might beat Matteo Renzi's ruling centre-left Democratic Party (PD) at the next elections, which are due by early 2018.

"Some of you may say that 5-Star uses double standards," Renzi wrote in an uncharacteristically forgiving Facebook post in which he did not call for Raggi to resign, but instead urged her to "do her job".

The nomination of Marra's brother, Renato, as director of tourism for Rome is the object of the probe, Raggi said in her Facebook post. Italy's anti-corruption office criticized the appointment of Renato Marra as a conflict of interest in December.

No further details about the investigation were immediately available.

(Editing by Catherine Evans)