The activist, whose real name is Stephen Yaxley-Lennon, was found guilty at London's Old Bailey court last week after he filmed defendants during a trial previous year and posted the footage on social media, breaching reporting restrictions on the case.
Robinson, real name Stephen Yaxley-Lennon, was found guilty of contempt of court a year ago and sentenced to 13 months in prison.
Dozens of his supporters have gathered on the streets outside the court, amid a heavy police presence.
After his sentence was announced, Robinson posted a message on his Telegram account and dismissed the judgement as a "joke" and urged his fans to protest "outside whatever prison I'm in on Saturday".
Passing sentence today, Dame Victoria Sharp said: "He [Robinson] has lied about a number of matters and sought to portray himself as the victim of unfairness and oppression".
Angry supporters of Robinson booed as news of his sentencing came in, with crowds chanting "we want Tommy out".
He wore a shirt emblazoned with the messages "convicted of journalism" and "Britain = North Korea".
She said the goal of sentencing for contempt was "punishment and deterrence" and said the court was also "concerned to demonstrate its determination to uphold the rule of law". The idea is that juries must not be influenced by anything but the evidence they hear in court.
He was found in contempt last week for breaching a reporting ban by videoing defendants accused of sexually exploiting young girls outside a courthouse in Leeds, northern England, while jurors were still considering their verdicts.
In May 2018, Yaxley-Lennon live-streamed a video outside Leeds Crown Court that contained information in breach of reporting restrictions.
Robinson, 36, was originally sentenced to 13 months in jail but was released two months later after an appeal.
Attorney-General Geoffrey Cox was given leave to relitigate the case, however, which he chose to do - resulting in Robinson being reconvicted, despite his defence team's arguments that his behaviour was "not materially different to the behaviour we see outside courts day in and day" from mainstream media reporters.
"Posting material online that breaches reporting restrictions or risks prejudicing legal proceedings is a very serious matter and this is reflected in the court's decision today", Cox said in a statement on Friday, when Robinson was found guilty.
She said that the objective of sentencing for contempt was "punishment and deterrence of the contemnor", adding: "The court is also concerned to demonstrate its determination to uphold the rule of law".
In an appearance on the far-right conspiracy theory website InfoWars on Monday, Robinson asked Donald Trump to grant him asylum in the United States of America, claiming he faced being killed in prison if he was jailed on Thursday.
He told Sky News outside the court that he wanted to move because people there "were behind him".
However he successfully appealed against the conviction and was released.
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