Today, BioShock fansite, Rapture Archives, had brought back Rapture Radio, after a year of being off the air. Partnered with Sonorous Inc., the radio station is filled with music heard in BioShock and BioShock 2, along with some additional songs between Rapture's timeline. You can find the station through the Rapture Archives museum section, under "Rapture Radio", along with the user manual.
Or, you can go directly to the station here:
Updates: since yesterday, more songs from the soundtracks are now being included into Rapture Radio, including the anthem, "Rise, Rapture, Rise". Soon enough, it'll be the Rapture station it should be.
05/04- Advertisements are now included in Rapture Radio.
05/05- Rapture Radio's tracklist is now included in Rapture Archives:
06/20- Due to two copyright holders ordering a take down notice, Rapture Radio is off the air until an agreement is made. Depending on a agreeable decision, there would be plans to hopefully bring it back on the 25th on 3PM EST, along with plans for KNO Radio, possibly another station that plays specifically songs from both BioShock games.
07/12- After a few days of it's announced return, Rapture Radio was indeed off the air. The host was bought out by a new owner, resulting in expensive fees and loosing out on their subscribers. However, it turned out to be a good thing on Rapture Archive's favor, since it's safe to say that it's now back on the air with a new system and a new host.