The English Defence League (EDL) founder, whose real name is Stephen Yaxley-Lennon, was handed a nine-month sentence at the Old Bailey on Thursday.
Dame Victoria Sharp told Robinson that the time he previously spent behind bars for the contempt will be taken into account, reducing his sentence to 19 weeks - of which he will serve half before being released.
Robinson, 36, of Luton, Bedfordshire, was found to have committed contempt of court on Friday, following a two-day High Court hearing held at the Old Bailey.
Dame Victoria and Mr Justice Warby found Robinson was in contempt in three respects when he filmed men accused of the sexual exploitation of young girls and live-streamed the footage on Facebook, in breach of a reporting ban, outside Leeds Crown Court in May 2018.
Giving reasons for the contempt finding on Tuesday, Dame Victoria said Robinson encouraged "vigilante action" in the video, which lasted an hour-and-a-half and was viewed online 250,000 times on the morning of the broadcast.
Throughout the Old Bailey hearing last Thursday and Friday, Robinson denied any wrongdoing, saying he did not believe he was breaching reporting restrictions and only referred to information that was already in the public domain.
But Dame Victoria and Mr Justice Warby found he was in contempt by breaching the reporting restriction imposed on the trial, by live-streaming the video from outside the public entrance to the court and by "aggressively confronting and filming" some of the defendants.
Robinson broadcast the footage while the jury in the second of a series of linked grooming trials was considering its verdict.
The video was eventually viewed 3.4 million times after being shared following his arrest.
A reporting restriction was in place which postponed the publication of any details of the case until the end of all the trials involving 29 people, in a bid to ensure all defendants received a fair trial.
Robinson was jailed for 13 months after being found in contempt of court on the day of the broadcast.
He served 10 weeks in jail before being freed after the original finding of contempt was overturned by the Court of Appeal in August 2018.
But the case was then referred back to the Attorney General, who announced in March that it was in the public interest to bring fresh proceedings against Robinson.
Dame Victoria and Mr Justice Warby gave permission for the Attorney General to bring a new case against Robinson at a hearing in May.