Users attempting to access the website Tuesday evening encountered an image of one of the Angry Bird characters with a U.S. National Security Agency logo and the text "Spying Birds," itv.com reported.
The developer of the game, Rovio, has denied collaborating with government agencies or making data available to them.
"Rovio Entertainment Ltd, which is headquartered in Finland, does not share data, collaborate or collude with any government spy agencies such as NSA or GCHQ anywhere in the world," the company said in a statement.
"As the alleged surveillance might be happening through third party advertising networks, the most important conversation to be had is how to ensure user privacy is protected," it said.
Documents leaked by former NSA contractor Edward Snowden suggest spy agencies have been using Angry Birds and other smartphone apps to harvest user data.
The NSA has issued a statement saying communications from anyone other than "valid foreign intelligence agents" is not of interest to the agency.
"Any implication that NSA's foreign intelligence collection is focused on the smartphone or social media communications of everyday Americans is not true," the statement said.