The website is registered to a person in Rhode Island and not Activision Publishing.
The site, which appears to be run by a group called Sn4gamers, asks users to share a link to the site on their Facebook page and elsewhere to receive a beta code.
Though the website may be fake, Modern Warfare 4 is in fact rumored to be in development. Captain Price voice actor Billy Murray reportedly confirmed the game was in development last year, with an additional report claiming Modern Warfare 4 is 2013's Call of Duty installment.
Activision confirmed last month that a new Call of Duty game will release this year. Executives do not expect this game be as commercially successful as immediate predecessor Black Ops II.