Arrest Warrant Issued For Russell Brand

New Orleans PD tells TMZ the misdemeanor warrant for simple criminal damage to property was issued tonight ... following Brand's run-in with a pap on Monday.

Brand is accused of grabbing the photog's iPhone and hurling it through the nearby window of a law firm.

As TMZ first reported ... people connected to Brand contacted the law firm and said the actor would be willing to pay for the damage to the window.