The controversial figure filmed defendants in a child grooming trial and broadcast it on Facebook in May previous year.
The maximum sentence for contempt of court is two years in prison, but it can also be punished with an unlimited fine.
Robinson was read the sentence Thursday at a courthouse in London and news of it angered his supporters gathered outside.
However, he had changed into a plain black T-shirt by the time he arrived in court with his legal team.
The video lasted an hour-and-a-half and was viewed online 250,000 times, after being live-streamed on Facebook.
Robinson filmed men accused of sexually exploiting young girls, breaching a reporting ban on the trial.
Police were then pelted with cans and plastic bottles as the group began chanting "we want Tommy out".
The attorney general said the sentencing illustrated how seriously the courts would take matters of contempt and urged everyone to think carefully about whether their social media posts could amount to contempt of court.
They said these were "not credible" and that he had "quite deliberately" broadcasted on the case, telling his viewers that it was the subject of reporting restrictions.
The sentencing hearing on Thursday was briefly delayed after Robinson, who arrived outside court accompanied by far-right commentator Katie Hopkins, was mobbed by supporters.
In an appearance on the far-right conspiracy theory website InfoWars on Monday, Robinson asked Donald Trump to grant him asylum in the U.S., claiming he faced being killed in prison if he was jailed on Thursday.
Dame Victoria added: "Robinson can not be given credit for pleading guilty".
The video was eventually viewed 3.4 million times after being shared following his arrest.
During the 2018 case at Leeds Crown Court, reporting restrictions had been put in place postponing the publication of any details until the end of a series of linked trials involving 29 defendants.
In a written ruling, Dame Victoria said Robinson had claimed his intention in making the broadcast was to "denounce the media" for their behaviour.
The nine months comprises six months for Robinson's actions outside Leeds Crown Court, and the activation of a separate three-month suspended sentence for similar actions at Canterbury Crown Court.
But the case was referred back to Attorney General Geoffrey Cox, whose decision to cite public interest in bringing fresh proceedings against Robinson was approved by High Court judges back in May.