It's the first time an airline has allowed customers to reserve flights on Facebook, although nearly all major U.S. airlines use Facebook and Twitter to promote sales.
Delta plans to expand the Ticket Window to other sites, including online banner ads from which customers could book directly.
The airline said the move, along with a redesign of its website delta.com earlier this week, is part of an overall effort to interact directly with its customers on the Web.
Big airlines like Delta, the world's largest, have been slower than their discount counterparts in catching the wave of social media. JetBlue and Southwest were the first to use social media for communicating with customers - dedicating staff to promoting their brands across cyberspace and dealing directly with individual complaints or complements on Twitter.
Delta, which is based in Atlanta, said there's still more changes to come on its website to make it more user-friendly. It's also working to improve the ease of use for its airport kiosks. It plans to launch an iPhone application within the next few weeks that will offer customers the ability to check in for flights, check flight status, review schedules, set a parking reminder, review frequent flier account balance and use electronic boarding passes in select cities.