Her victory would be a blow to Italy`s Prime Minister Matteo Renzi.
His PD party may also lose in Italy`s financial capital, Milan, and faces tough battles in Turin and Bologna.
Ms Raggi, a 37-year-old lawyer, won 35% of the vote in the first round two weeks ago, against 24% for Mr Giachetti.
Correspondents say a victory in Rome would give anti-globalist Five Star a platform for parliamentary elections due in 2018.
When in Rome shake up the politics
The next mayor of Rome will find a city mired in debts of more than €13bn (£10bn; $15bn) - twice its annual budget.
Romans are frustrated by potholes, piles of rubbish and serious deficiencies in public transport and housing, the BBC`s James Reynolds in reports from the Italian capital.
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