Steering using the keyboard is possible, but due to the simulation nature of the game, very difficult and uncomfortable. This is because the keyboard offers only "binary" control - you either have gas pressed to the metal or zero power. The same applies to brakes and turning - the tires are either directed straight ahead or fully to the left or right. One way to get rid of this effect is to quickly press the gas or brake keys, allowing you to have bigger control over the vehicle, but this requires a lot of practice. While using the keyboard you should turn on the assists that the game offers: ABS, Traction Control and Stability Control.
Ultimately, it is a good idea to purchase a gamepad or preferably a steering wheel.