Robinson, whose real name is Stephen Christopher Yaxley-Lennon, was locked up in May after he filmed people involved in a criminal trial and broadcast the footage on social media.
The footage, lasting around an hour, was watched 250,000 times within hours of being posted on Facebook.
The far-right activist was given 10 months for contempt of court, which he admitted, and a further three months for breaching a previous suspended sentence.
The 35-year-old will make a bid to have his sentence cut at the Court of Appeal in London, where a hearing is expected to take place on July 24.
Robinson was detained outside Leeds Crown Court in May after using social media to broadcast details of a trial which is subject to blanket reporting restrictions.
Jailing him, Judge Geoffrey Marson told Robinson his actions could cause the trial to be re-run, costing “hundreds and hundreds of thousands of pounds”.
The judge said it was a “serious aggravating feature” that he was encouraging others to share it and it had been shared widely.
He added: “Everyone understands the right to freedom of speech but there are responsibilities and obligations.
“I am not sure you appreciate the potential consequence of what you have done.
“People have to understand that if they breach court orders there will be very real consequences.”
It was the second time Robinson had breached court orders, having narrowly avoided jail in May 2017 over footage he filmed during the trial of four men who were later convicted of gang-raping a teenage girl.
The judge on that occasion gave him a three-month suspended sentence and told him his punishment was not about “freedom of speech or freedom of the press” but about “justice and ensuring that a trial can be carried out justly and fairly”.
During Robinson’s sentencing hearing, his barrister Matthew Harding said the activist had “deep regret” for what he had done and “did not try to cause difficulties for the court process”.