The group, known as Anonymous, has vowed to launch a so-called cyber war unless police officers implicated in the Thomas incident are prosecuted, the police chief resigns and the Thomas family is given $5 million.
The 37-year old died on July 5, days after a violent confrontation with police. The incident is being investigated by the Orange County District Attorney and the FBI.
A police spokesperson said the city's I.T. has been alerted as a precaution, but they were not sure how credible the threat was.
David Perry, a cyber security expert, said the hackers may try to bring down the website and email.
"Possibly even malware to bring down servers and other sites inside the city of Fullerton," he said.
Perry said if the group does carry out the cyber attack, they will surely be busted and face federal charges.
Dozens of protesters showed up outside the Fullerton Police Department on Saturday to demand justice. Demonstrators are calling for the release of police video of the confrontation.
"Well the importance of releasing the tape is for public knowledge. We want to know the truth, the absolute truth of what had happened," said Thomas's father Ron Thomas.
Acting chief of police, Capt. Kevin Hamilton, released a statement Saturday that said, "We respect the concerns of the Thomas family and the rights of the protesters and understand the sentiments of the community. If officers are found to be criminally or administratively culpable, they will be held accountable."