The team, who have Spaniard Fernando Alonso and Finland's Kimi Raikkonen as their drivers in a line-up of world champions, have half a million facebook 'likes' while the carmaker has 12.6 million.
The official Ferrari Twitter account (@InsideFerrari) has more than 670,000 followers.
Ferrari finished third overall in the constructors' championship this season, behind champions Red Bull and Mercedes, although Alonso was runner-up in the drivers' standings.
President Luca Di Montezemolo told reporters at a Christmas lunch at the Fiorano test track that he was looking forward to the new driver pairing and expected them to work well together.
Ferrari presented their new engine, designated the 059/3, in virtual fashion with a 3D film shown at the Maranello factory on Thursday.
Engine and electronics head Luca Marmorini told reporters that reliability and economy would be the major concerns for all teams in the new era with drivers having to make 100kg of fuel last an entire race.
"It will be relatively easy to finish with 100kg in some races, others will be more challenging," he warned. "100kg in Melbourne and 100kg in Monaco are not the same at all."
(Editing by Ed Osmond)
