Judge James Brandlin, from the superior court of Los Angeles, turned down a request from Polanski's lawyers, who wanted a new hearing to try and close the case on procedural grounds.
Brandlin said the request had no constitutional basis, and the Academy Award-winner had even less right to the procedural hearing than he did when he fled justice 37 years ago.
In a nine-page ruling, the judge also noted that the US had consistently asked for Polanski's extradition.
In 1977, the filmmaker, then aged 43, was accused of raping Samantha Geimer after a photo shoot.
He pleaded guilty to unlawful sex with a minor, or statutory rape, avoiding a trial, but then fled the country fearing a hefty sentence.
US officials have pressed for his extradition regularly to no avail.
Last October, US authorities unsuccessfully sought his arrest while he was in Poland.
In September 2009, Polanski, who became a French citizen in 1976 after moving there from Poland, was arrested in Switzerland on an international arrest warrant. After being held for months, Polanski was released.
Geimer wrote a book about her encounter with Polanski last year. Geimer wrote she was made to drink champagne and was given a sleeping pill before being raped by Polanski in the house of actor Jack Nicholson.
Polanski's work includes "Rosemary's Baby," "Chinatown," and "The Tenant".