The woman says hat despite the San Francisco-based company's claim that it maintains high safety standards, there was no practice of adequate screening of its drivers which puts at risk the safety of commuters.
Reports said the suit was filed on Thursday in U.S. District Court for the Northern District of California.
A professional, the 27-year-old woman was returning home in the cab. The accused allegedly preyed on her when she dozed off.
Uber was banned in Delhi after the incident which led to the arrest of its driver Shiv Kumar Yadav. However, it began operating in the capital on December 6.
Police says Yadav has criminal records of committing crimes against women in the past.
"Uber's focus on its bottom line over the safety of its passengers has resulted in what can only be described as modern-day electronic hitchhiking," Douglas H. Wigdor, the woman's lawyer, said in a statement.