Robinson's video, which was eventually viewed by 3.4 million, was originally broadcast while the jury considered its verdict on the grooming gang trial.
The maximum sentence is two years' imprisonment.
Supporters of Yaxley-Lennon gathered outside the London court and booed as news of his sentence reached them.
However, he had changed into a plain black T-shirt by the time he arrived in court with his legal team.
It relates to a Facebook Live broadcast he made outside the trial of a sexual grooming gang at Leeds Crown Court in May 2018 for which reporting restrictions had been put in place to ensure the 29 defendants were given a fair trial.
Robinson filmed men accused of sexually exploiting young girls, breaching a reporting ban on the trial.
The crowd marched towards the Old Bailey chanting "we want Tommy out" before some began pelting police with bottles and cans.
The judge said the words he used in the video would have been understood by viewers as "an incitement" to harass the defendants and "gave rise to a real risk the course of justice would be seriously impeded".
She said that the goal 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".
And then seemed to contradict the plea, with another plea for cash donations from his supporters, in a video filmed ahead of his sentencing on Thursday.
Ahead of the hearing, Robinson asked Donald Trump to grant him asylum in the US.
"The respondent can not be given credit for pleading guilty".
Throughout the Old Bailey hearing, 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.
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.
The case was subject to blanket temporary reporting restrictions under the Contempt of Court Act 1981 to avoid a "substantial risk of prejudice" to the trial, which involved multiple defendants and was linked to other linked proceedings.
However, after serving two months in jail, his original case was overturned by the Court of Appeal.
Dame Victoria Sharp said Robinson's previous time in jail had been taken into consideration, reducing his sentence to 19 weeks - of which he will serve half before being released.
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.