But critics question whether it will have any practical effect on jurors who are constantly on sites such as Facebook and Twitter, and suggest judges vet the social media activity of potential jurors before seating them.
"If you have an Internet addict who just can't psychologically stop, you may want to excuse that person," said Paula Hannaford-Agor, who studies juries at the National Center for State Courts.
Brian Walsh, presiding judge for Santa Clara County Superior Court, said a fine could also change the dynamic between judges and juries.
"You want to present the jurors' obligations to serve as an inviting opportunity to participate in the democratic process," he said. "One could consider it counterproductive to be laying out all the penalties a juror can incur if they blow it."
It is not clear exactly how many times juror social media or Internet use has affected trials. But anecdotal evidence suggests it is more than sporadic.
Eric Robinson, co-director of the Press Law and Democracy Project at Louisiana State University, said he used to track cases of juror social media or Internet misconduct using news accounts and other sources, but there were so many "it got to be more trouble than it was worth."
"Those are the ones we hear about," he said. "I'm sure it happens a lot more."
An Arkansas court in 2011 threw out a death row inmate's murder conviction in part because of tweets. One said "Choices to be made. Hearts to be broken." Another said "It's over" less than hour before the jury announced its verdict.
A New Jersey appeals court in 2014 tossed the heroin possession conviction of two men after a juror was accused of searching the defendants' names online and finding information about their criminal records.
A California appeals court in January cited juror Internet research in throwing out a fraud conviction against an investment firm CEO. The juror looked up a case involving an accountant the defendant blamed for the fraud.
Judges warn jurors against using social media and the Internet, and have the power to hold them in contempt if they violate those rules.
Greg Hurley, a lawyer who studies juries at the National Center for State Courts, said he is unaware of any state that fines jurors outside the contempt process.
California judges say the contempt process can be time-consuming and is rarely invoked. A juror facing contempt has a right to an attorney, and the court could get bogged down in a lengthy formal hearing. So judges often opt to replace a wayward juror with an alternate to keep the proceedings moving.
"Historically, contempt has been something judges are told, 'Don't do,' " said J. Richard Couzens, a retired judge from Placer County who now rotates through courts around the state. "You have to follow so many rules to institute a contempt process."
Couzens, a member of the judicial committee that recommended the fines legislation, said he dismissed a juror years ago in a theft case for using a cellphone to figure out the value of a stolen item.
The fine would be similar to a traffic citation, making it relatively easy to dispense, Couzens said.
Judges could mention it when warning jurors against Internet and social media use, said Steve Austin, presiding judge in California's Contra Costa County.
"At the very least with the sanction, it would be a good thing you'd be able to tell the jurors," he added.
The legislation initially called for giving all state judges the power to fine wayward jurors. But it was scaled back after legislators expressed concern that it could dissuade potential jurors from serving.
The bill now authorizes the judiciary to select some county courts for a five-year pilot program, which a legislative analysis said could save participating courts money.