"We, Anonymous around the world, have decided to declare war on you the terrorists," it said.
The video is described as a message for "al Qaeda, the Islamic State and other terrorists," and promises to avenge the killing of 12 people in Wednesday's attack.
"We intend to take revenge in their name, we are going to survey your activities on the net, we are going to shut down your accounts on all social networks," Anonymous said.
Said spent several months in Yemen in 2011, receiving weapons training and working with Al Qaeda in the Arabian Peninsula, U.S. officials said Friday.
His younger brother Cherif was sentenced to three years in prison for being part of a jihadist recruitment ring in Paris that sent fighters to join the conflict in Iraq.
An ISIS radio broadcast Thursday praised the attackers, calling them "brave jihadists." But the broadcast did not say whether the two had any connection to the militant group.
The attack has prompted an outpouring of solidarity, with thousands joining rallies in defense of freedom of speech and republishing many of the magazine's most controversial cartoons -- including of the Prophet Mohammed.
Anonymous has hacked websites belonging to government departments, companies and other organizations. The loose collective is also known for supporting the Occupy movement.