Japanese prosecutors investigated the incident but dropped the case in November without giving a reason.
The rape case is the latest in a string of allegations to hit US forces based in Japan, triggering a wave of public protest against the American presence in the country.
Last week Japanese prosecutors dropped the case of another US Marine accused of raping a 14-year-old girl on the southern island of Okinawa.
Officials said the girl did not want to continue the case, but the US military has said the 38-year-old Marine alleged to have carried out the attack has been taken into custody and faces potential disciplinary action.
Okinawa is home to more than half the 40,000 US troops based in Japan.
Japan is the top US ally in Asia but anger over the conduct of American troops based in the country has strained relations.
Last week Condoleezza Rice, the US secretary of state, apologised on a visit to Tokyo over the alleged rape during meetings with Japanese government officials.
The US military meanwhile has been keen to be seen taking a tough line on discipline, placing a sweeping curfew on troops and their families based in Iwakuni and Okinawa.