The former England and Manchester United captain, who now plays for Major League Soccer's DC United, was arrested on 16 December in Virginia.
A spokesman for Loudoun County Sheriff's Office confirmed Rooney was taken into custody "on a charge of public intoxication stemming from an arrest by the Metropolitan Washington Airports Authority Police".
The spokesman added: "He was later released on a personal recognizance bond."
Court documents show that Rooney, 33, was released after paying a $25 ($NZ37) fine and $91 ($NZ135) costs.
Rooney was banned from driving for two years in September 2017 after he was found to be almost three times over the legal limit when he was stopped by police in Cheshire.
He started his career with English Premier League club Everton in 2002, before joining Manchester United under Sir Alex Ferguson in 2004.
Rooney made 393 appearances for United in his 14 years with the club, scoring 183 goals, before rejoining Everton for a season in 2017.
At the international level, Rooney played 120 matches for England.
The following year, he moved to the US in June 2018 after signing a three-and-a-half-year contract with DC United.
Rooney led the club to the play-offs in his first season before they suffered a first-round loss.