The SCOTUS dose not allow cameras in the courtroom during oral arguments. Since 1946, the Federal Rule of Criminal Procedure 53 has prohibited electronic media coverage of criminal proceedings in federal courts. [1]
Begining in 1955, the SCOTUS began recording audio of oral arguments to be used by justices, their law clerks, researchers at the National Archives [2]. These recourdings where used for educational and research purposes only and no copies where made [2]. University of California political scientist Peter Irons released six audio cassettes with transcipts of excerpts from oral arguments in 1993 [3]. After considered legal remedies against Irons, the court changed their policy allowing no limits on the use of the archive recordings [3].
During the 2010-2011 term, the Supreme Court begain releasing the audio of oral arguments for the week on Fridays after conference [4]. Before this, audio was not available to the public until the start of the next term [4]. Audio of opinions are not released until start of the next term.
[1] http://www.uscourts.gov/about-federal-courts/cameras-courts/history-cameras-courts
[3] https://www.oyez.org/about-audio
[4] https://www.supremecourt.gov/oral_arguments/argument_audio/