Starbucks plans to give away 50 million free digital songs to promote a new wireless iTunes music service that’s about to debut in select markets. Unfortunately – they’re picking the songs.

From Oct. 2 to Nov. 7, baristas in the company’s more than 10,000 U.S. stores will hand out about 1.5 million “Song of the Day” cards each day. The cards can be redeemed at Apple’s online iTunes Store.

Thirty-seven artists with featured songs include Paul McCartney and Joni Mitchell ‚Äî the first two to sign on with Starbucks’ Hear Music label ‚Äî along with Joss Stone, Dave Matthews, John Mayer, Annie Lennox and Band of Horses. The first song will be Bob Dylan’s Joker Man.

Earlier this month, Starbucks and Apple announced a partnership that will allow users of Apple’s iPhone and new iPod Touch to download songs playing in a Starbucks shop directly to their portable devices. The service will launch at 600 shops in Seattle and New York on Oct. 2, then roll out in San Francisco in early November.

Starbucks plans to have the service up and running in a quarter of its stores by the end of next year and in all U.S. stores with wireless networks by the end of 2009. There are no immediate plans to expand the service to international markets.