Lukaku was arrested on July 2 at around 8pm after five verbal warnings at a Beverly Hills home in the summer.
The striker can send a lawyer in his absence to Los Angeles Airport Courthouse.
Just a week after the incident, Lukaku signed for Manchester United in a £90m move from Everton.
The 24-year-old has made a huge impact at Old Trafford since his arrival and scored in the 4-0 win over Crystal Palace on Saturday.
Lukaku is currently the Premier League's top scorer with seven goals.