A report in The Wall Street Journal newspaper says the small Internet provider, www.Sonic.net, fought the order and lost, and was forced to turn over the information about Jacob Appelbaum.
It says the request included the e-mail addresses of the people that Appelbaum had corresponded with over the last two years, but not the full e-mails.
The 28-year-old Appelbaum, who is a developer at a nonprofit that helps people maintain anonymity online, has not been charged with any wrongdoing.
The newspaper says Google declined to comment.
Debate has centered on whether the law, the Electronic Communications Privacy Act, violates constitutional protections against unreasonable search and seizure. The act allows the government to secretly obtain information from people's e-mail and cell phones without a warrant.
The United States has said it is pursuing an active criminal investigation against WikiLeaks, the anti-secrecy website that has published thousands of sensitive U.S. diplomatic cables and documents related to the wars in Iraq and Afghanistan.