They said they had new evidence showing "judicial and prosecutorial misconduct" had distorted the legal process.
Polanski, 75, has lived in France since fleeing the US in 1978 to avoid facing a prison sentence after pleading guilty to having sex with a 13-year-old girl.
He was initially indicted on six felony counts and faced up to life in prison.
Since then, Polanski has been unable to return to the US for fear of arrest, and has even avoided making films in the UK because of the danger of extradition.
The arrest warrant for him is still in effect, barring him from re-entering the US. Interestingly the child in question, now a 43-year-old woman, has said that she wants the charge dropped and that he should be allowed back into the US.
In a motion filed with the Los Angeles County Superior Court, lawyers for the Polish-born director said a recent documentary about him had revealed that "judicial and prosecutorial misconduct... so distorted the legal process that the interests of justice can only be served with complete dismissal of the case".
The HBO documentary, "Roman Polanski: Wanted and Desired," portrayed Judge Laurence J. Rittenbrand, who presided over the trial, as a publicity seeker who held news conferences and engaged in extra-judicial meetings about the case.
In an interview for the film, former Los Angeles County Deputy District Attorney David Wells admits having advised the Judge Rittenband on how to sentence Polanski, even though he was not assigned to the case.
Polanski's lawyers, Chad Hummel and Brad Dalton, said the documentary had uncovered "a pattern of misconduct and improper communications" between prosecutors and the judge.
In their brief, the lawyers said that Mr Wells' recommendation to send Polanski away for a diagnostic study was illegal without his lawyers present. They said Mr Wells also inflamed the judge by showing him photos depicting the director with girls at an Oktoberfest party in Germany while he was awaiting sentencing. They said the photos were misrepresented.
"As the result of DDA Wells' illegal ... communications, Mr Polanski has been subject to a punishment that has spanned the course of over 30 years," the motion stated, noting he has been deprived of opportunities to work on films outside France.
"This case serves as a classic example of how our justice system can be abused, and defendants' rights trampled, by an unholy alliance between courts and criminal prosecutors," they added.
Polanski has continued to direct films while in exile, including the 2002 Holocaust drama 'The Pianist,' for which he won the best-director Oscar Academy Award.
Sandi Gibbons, spokeswoman for Los Angeles District Attorney Steve Cooley, said her office had not been served with the motion and heard about it only through media reports. She said the office could not take a position until they see the legal papers.
"As far as we're concerned it is a matter between Mr Polanski and the court," Sandi Gibbons told Reuters.
Ms Gibbons said Polanski was a fugitive and that there was still a warrant out for his arrest. A hearing is scheduled for 21 January.