Ten minutes after his maiden tweet he had 10,000 followers. His next 10,000 came in the following half-hour.
(Read more: Twitterverse reacts to Apple chief's first tweet)
Cook was slowly adding people to follow as well, with Anderson Cooper, Kings of Leon, Jimmy Fallon and Duke Basketball among his first 10. One other is Steve Jobs' widow, Laurene Jobs, whose Twitter presence is enigmatic—she's never tweeted and follows no one. She does, however, have more than 2,000 followers.
Apple's new iPhones—the 5S, with new features including a fingerprint scanner, and the lower-priced 5C in pastel colors—went on sale at stores Friday, luring the now-familiar long lines of fans at Apple stores everywhere.
(Read more: Record iPhone debut is not a 'victory lap' yet: Pro)
Billionaire investor Carl Icahn recently spurred investors to pump up Apple's market value by some $17 billion after he tweeted—in his 11th tweet ever—that he had "a large position" in the Cupertino, Calif.-based company.
—By CNBC's Matt Twomey. Follow him on Twitter @Matt_Twomey.