The US Government has ordered a web hosting service to disclose information about visitors to an anti-Donald Trump website, raising fears about privacy online.

The Department of Justice issued a warrant asking for the details of people who own, operate and have visited the DisruptJ20 website, which coordinated protests at Trump's inauguration.

In a request served to website hosting company DreamHost, the Department called for the IP addresses and computer information of 1.3 million visitors, as well as the time they visited.

"That information could be used to identify any individuals who used this site to exercise and express political speech," said DreamHost. "That should be enough to set alarm bells off in anyone's mind."

The details requested do not include visitors' names, but could be used to uncover the identities of those who had not used a privacy tool when browsing.