Rooney was arrested on December 16 by the Metropolitan Washington Airports Authority Police (MWAA), the agency that operates Reagan National and Dulles International airports.
However, he was released on a personal recognizance bond, according to Loudoun County media relations and communication manager Kraig Troxell, as per CNN.
According to online court information, the charge was for "public swearing/intoxication," a misdemeanour crime under Virginia law.
The 33-year-old who is ranked as England and United's all-time record goalscorer is currently playing for MLS's DC United team.
In a statement, his spokesman said, via BBC Football: "During the flight, Wayne took a prescribed amount of sleeping tablets mixed with some alcohol consumption and consequently was disorientated on arrival.
"He was approached by police who arrested him on a minor misdemeanour charge.
"He received a statutory automatic fine and was released shortly afterwards at the airport. The matter is now at an end.
"Wayne would like to put on record his appreciation for the manner he was treated by all involved."