Mary Kaya, from Batley, had around 30 followers on her Twitter account when she retweeted a link to an audio clip by Abu Bakr al-Baghdadi, Leeds Crown Court heard.
Kaya, 57, denies posting the link and said she only uses social media to find out what is going on in the world.
Simon Davis, prosecuting, told a jury of 10 women and two men that the defendant’s previous address in Dewsbury was searched by counter terrorism police, who arrested her husband in May 2014.
Computer equipment was seized and an investigation into Kaya’s activity on the internet began later the same year, the court heard.
Mr Davis said monitoring of Kaya’s Twitter account, named Justice and with the handle @GardenofGold, showed that the link to al-Baghdadi’s speech, Even If The Disbelievers Despise Such, was retweeted on November 13 2014.
The barrister said: “The message was aimed at encouraging anyone who listened to or read it to participate in terrorist activity.”
Mr Davis said the speech stated there was an obligation upon Muslims to engage in violent jihad and that anyone not behaving in that way would face devine retribution.
The court heard that the seized computer was used to search for and view information about radical Islamic preachers, supporters of IS, people who had travelled to Syria and footage of explosions and vicious attacks.
Mr Davis said the person using the computer also visited a number of Twitter accounts which were “generally supportive of Islamic State”.
The barrister said the @GardenofGold Twitter account posted “well-written, eloquent tweets” and sometimes engaged in conversations with other social media users, including an English Defence League supporter.
Kaya was arrested and interviewed on October 21 2015.
Mr Davis said the defendant told police the computers and phones seized from her home would not have any terrorist material on them and she used Twitter “to see what was going on in the world”.
The court heard that Kaya said no-one else used her account so she was the only person responsible if any material was found.
In a second interview in January 2016, Kaya made no comment but provided a prepared statement in which she said she had never posted anything on her Twitter account and believed the account had been hacked, the jury was told.
Mr Davis said she now claims someone else must have had access to her account.
He said: “The prosecution allege it is no coincidence that the Twitter account retweeted the publication Even If The Disbelievers Despise Such, when you consider the other material on the account.”
He continued: “The irresistible conclusion to be reached is that which the defendant first stated in interview: ‘No-one else uses my account so if there’s anything on there, I’m the only one guilty’.”
Kaya denies one charge of dissemination of a terrorist publication likely to encourage people to participate in terrorism.
The trial was adjourned until Tuesday.