Robinson turned himself in to authorities after an extensive manhunt following Kirk’s shooting at an open-air event at Utah Valley University in September.
He confessed to the crime to his father who recognised him from images released by authorities and who eventually persuaded him to surrender.
On Thursday, Robinson arrived in court with restraints on his wrists and ankles.
He wore a dress shirt, tie and slacks and smiled at family members sitting in the front row of the courtroom, according to the BBC’s US news partner CBS. His mother, father and brother were in court with him.
A coalition of national and local news organisations wants to preserve media access to the case, arguing for transparency and public accessibility. They are pushing for the release of a recording and transcript from an October hearing in the case.
Kirk’s widow Erika Kirk, who has been combatting conspiracy theories about her husband’s death, has also asked for transparency in the case. On Fox News last month she said that “we deserve to have cameras in there”.
Part of the hearing on Thursday is to review a 14 October audio recording and a 24 October transcript of hearings that were closed to the public. Another section of the hearing was streamed online for public viewing.
“I need to hear what should or should not be sealed or protected and it would not benefit to have everyone listen to what should be sealed,” Judge Tony Graf said.
He plans to issue a ruling later on Thursday.
In October, the judge allowed Robinson to wear civilian clothes during pre-trial hearings to avoid prejudicing potential jurors, but he required Robinson to wear restraints during hearings.
Photo or video of him in restraints have been barred.
