In her lawsuit, the Indian woman accuses Uber of putting profits over safety, calling the US-based company the "modern day equivalent of electronic hitchhiking".
In an email to AFP late Thursday, the American lawyer for the 25-year-old woman, who cannot be named for legal reasons, said Uber was being sued for unspecified damages for "physical and emotional harm".
"Despite its self-proclaimed commitment to safety, opening the Uber app and setting the pick-up location has proven to be the modern day equivalent of electronic hitchhiking," according to the lawsuit filed in a court in California.
"Buyer beware - we all know how those horror movies end," the lawsuit said, accusing Uber of negligence.
The woman's lawyer, Douglas H Wigdor, had earlier represented a hotel maid who accused former International Monetary Fund chief Dominique Strauss-Kahn of sexual assault in 2012.
The San Francisco-based company did not comment on the lawsuit but said "our deepest sympathies remain with the victim of this horrific crime".
A spokesman said the company was also "cooperating fully" with authorities to ensure the person responsible for the crime was brought to justice.
Uber was banned from Delhi's streets in the aftermath of the December 5 attack on the woman, which sparked new safety fears in a city with a high record of sexual violence.
The trial of the accused driver, who allegedly attacked the woman as she was on her way home from dinner, is underway. He has pleaded not guilty to charges of rape, kidnap and criminal intimidation.
Uber, which connects passengers to drivers through smartphone apps, last week said it was resuming its Delhi operations, but authorities rejected its request for a licence to operate as a radio-taxi company.
Uber has said it is committed to protecting its passengers in India and globally.
India is one of the company's key markets outside the United States and operates in nearly a dozen Indian cities.
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Rapes that come to light in the media are the ones that are reported. It depends on a functioning legal system.
@Proudpakistani: Truly sad. They are all busy tut-tutting Pakistan on the Shikarpur killings, while their women cry hoarse over gang-rapes everyday.
Rape is the now the new favourite hobby of indians after pakistan / islam bashing and commenting on ET