According to BBC News, Polanski's legal team are citing judicial misconduct in the filmmaker's 1977 US trial as the basis for the plea.
The appeal, filed on Thursday in Los Angeles, asks that a special counsel investigate the judge's alleged unlawfulness.
Polanski's lawyers say that former Deputy District Attorney Roger Gunson testified in secret about the judge's conduct earlier this year. They are requesting that transcripts of Gunson's testimony be released.
The director is currently under house arrest in Switzerland and faces a US arrest warrant for his conviction of unlawful sex with a 13-year-old girl.
Polanski has been ordered to appear in court in Los Angeles to be sentenced.
The Swiss government is apparently awaiting the outcome of any appeals before it decides to extradite him to the US.