I have recently bought the game on Steam. When i plugged a USB game controller into my PC. I booted up my game. However, steam states it can be played with a controller but in menu options there is no ability to key bind my controller. What is up with this?
Yes, you can.
On the Borderlands 2 page on Steam it says "Full controller support" meaning that it will be compatible with a Xbox 360 controller or any other controller that works with PC and is supported by Steam.
However, as far as I can see your controller is not supported. But @5pike's solution to use x360ce should work.