Now that Anonymous has declared cyberwar against the so-called Islamic State in retaliation for the Paris terrorist attacks, the question becomes: What can the hacker group actually do?

Taking over and shutting down Twitter accounts is a logical first step. But the real prize, experts say, is in fundamentally disrupting the militant group's recruiting mechanism. ISIS pitches its radical Islamist message through e-mail, Web chat, Skype calls and YouTube videos, and more recently it promoted a mobile messaging app called Telegram.

An Anonymous spokesman in a trademark Guy Fawkes mask said in a still unverified YouTube clip that the group "will launch the biggest ever operation" against ISIS, according to transcripts of the French video.

A man wearing a mask associated with Anonymous makes a statement in this still image from a video released on social media on November 16, 2015. Reuters

Anonymous, a 12-year-old virtual community that's been linked to hacks on everything from the government of Zimbabwe and Bay Area Rapid Transit to Visa, MasterCard and the Federal Reserve, has proven plenty capable of following through with its threats.

One approach Anonymous could take is to shut down online accounts and thus undermine ISIS' recruiting tools. Another is to embarrass ISIS by publishing evidence of the hypocrisy among its leaders, said Jonathan Sander, vice president of product strategy at cybersecurity company Lieberman Software.

"When they go recruit, they're hugely dependent on their online presence," Sander said of ISIS. "If Anonymous takes all that out, it's like capping the revenue of a company. They trade in the lives of poor misguided people."

Read More: After Anonymous, UK threatens ISIS with cyberattack

The U.K.'s Independent reported that Anonymous has already started leaking information about ISIS members, and the publication said it's seen one post that includes the address of a recruiter in Europe. Using the Twitter handle @opparisofficial, Anonymous said on Tuesday that more than 5,500 Twitter accounts for ISIS are down.