Former Roger Stone associate Andrew Miller had challenged Mueller's appointment last year after he failed to comply with a subpoena served to him by a federal grand jury.
"Because the Special Counsel is an inferior officer, and the Deputy Attorney General became the head of the Department by virtue of becoming the Acting Attorney General as a result of a vacancy created by the disability of the disability of the Attorney General through recusal on the matter, we hold that Miller's challenge to the appointment of the Special Counsel fails," the court document said.
As a result of the ruling, the court continues to find Miller in civil contempt, the court document said.
In some cases, according to US law, a witness held in contempt can be sent to jail until they agree to testify.
Mueller is investigating allegations of Russian interference in the 2016 election and any connections between Moscow and the Trump Campaign. Russia has repeatedly denied all allegations of interference, and both Trump and Moscow have denied any collusion during the campaign.