Russell Brand isn't out of the fire for tossing a paparazzo's iPhone -- New Orleans police have issued a warrant for his arrest.
New Orleans PD tells TMZ a 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 window of a nearby 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.
Russell is still in New Orleans filming a movie. We contacted a rep for the production ... who refused to comment on the warrant.