The couple was in front of a home that Cage insisted they were renting, police said. When she said it wasn't theirs, Cage grabbed her arm, according to a police news release.
Cage started hitting vehicles and tried to get into a taxi, police said. An officer saw that Cage was drunk and told him to get out of the cab. Cage then started yelling at the officer.
The actor has been booked on charges of domestic abuse battery, disturbing the peace and public drunkenness. He was released on $11,000 bond Saturday.
Representatives for Cage could not immediately be reached Saturday.
Cage has been a frequent visitor to New Orleans, where he has owned property and shot movies. He has also had financial troubles, despite being one of the highest-paid stars in Hollywood.
He had been behind on taxes and has said he's had to sell numerous assets because of his finances. He sued his former business manager in October 2009 for $20 million, claiming the man's advice led him to financial ruin.
Cage won an Academy Award for his performance in 1995's "Leaving Las Vegas."
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