The order involved a government investigation of Jacob Applebaum, a volunteer with WikiLeaks, who has not been charged with any crime.
Fighting the order was "rather expensive but we felt it was the right thing to do," Jasper told The Wall Street Journal.
Sonic appealed to block the order but lost in its bid to do so.
Since U.S. Attorney General Eric Holder said the Justice Department is investigating WikiLeaks, Sonic and Google have received orders to turn over the e-mail addresses of people who have used the Internet to correspond with Applebaum, but not the e-mails themselves, the Journal reported Monday.
Google has not commented on the issue, the Journal said.
The order was issued under the Electronic Communications Privacy Act written in 1986, three years before the World Wide Web was envisioned.
Some say the request is akin to asking a company to turn over an individual's personal address book.
The government argues the request is more aligned with asking for a public phone book than a personal one. However, the court orders can be issued in secret. Both Sonic and Google petitioned for permission to inform Applebaum of the investigation but the law is set up in a manner that prohibits this.
Google, Microsoft Corp. and AT&T are among the firms lobbying to update the law.
Sen. Patrick Leahy, D-Vt., said in May the law was "significantly outdated and outpaced by rapid changes in technology."
Leahy has introduced a bill to update the law.