Fans have until December 19 to vote for their favourite alternative cover on the studio's official website.
Check out the Bioshock Infinite reversible cover designs below:
Copyright: 2K GamesIn addition to the covers featured in the poll, studio head Ken Levine confirmed that more alternative covers would be available to print closer to launch.
"I'm happy to announce that the game will come with a reversible cover," writes Levine.
"But that's not all. We want to hear your voice on what that cover should be. To that end, we've arranged a poll that lets you choose from several potential reversible covers.
"I've got my favourite, but I'm not telling which. We've got to do this quickly to meet our print deadlines, so vote soon. Like, NOW!
"But what's that you say? You want even more choice in covers? We're also going to be arranging a whole mess of MORE alternate covers which will be available to download and print yourself.
"Of course, these are free and we'd love to hear your thoughts in the forums as to what you'd like to see," he added.
The original BioShock Infinite box artwork, which was criticised by fans, depicts protagonist Booker DeWitt wielding a firearm with a burning American flag and an airship in the background.
BioShock Infinite was originally slated for release in October 2012, but has run into several delays and will now land on March 26, 2013.
The game will be released for PlayStation 3, Xbox 360 and PC.
Watch a trailer for BioShock Infinite below: