The request is expected to reach the high court Friday.
Spector's attorneys say the music producer's constitutional rights were violated during the trial.
His lawyer contends the trial judge became a witness for the prosecution by offering his opinion on an expert's testimony.
The same arguments were made to state appellate justices, who refused to consider them.
The appellate justices upheld Spector's second-degree murder conviction in the death of actress Lana Clarkson.
Spector is serving 19 years to life in prison.
The Associated Press contributed to this report.