The anticipated first-person game previously held the No. 2 sales rank at Amazon's Computer & Video Games division. Wii has held the No. 1 sales rank since Aug. 17.
The title landed in the top 10 last week at the retailer following the debut of a first level demo on the Xbox Live Marketplace.
Bioshock, set for release on the Xbox 360 and PC on Aug. 21, is a first-person shooter that allow players to genetically alter their body to don new powers.
The PC version currently ranks at No. 7 at Amazon.com.
Microsoft this month price cut all Xbox 360 hardware models from $20 to $50 in the U.S. The price cut coincides with key game releases in Aug., including EA's Madden NFL 08, 2K's Bioshock, and Midway's Stranglehold.
Microsoft has sold 5.6 million Xbox 360 units to date in the U.S.