Taken from the Occulus Rift website FAQ.
What are the minimum requirements and recommended specifications for the Oculus Rift Development Kit 2?
Minimum requirements: A computer running a Windows 7 or Windows 8, Mac OS 10.8 or higher, or Ubuntu 12.04 LTS operating system, 2 USB ports (at least one powered), and a DVI-D or HDMI graphics output.
Recommended specifications: A desktop computer running a dedicated NVIDIA GeForce GTX or AMD Radeon graphics card with DVI-D or HDMI graphics output, with capability of running current-generation 3D games at 1080p resolution at 75 fps or higher.
The recommended specs roughly translate to a R9 290X or GTX 970 or better. And I'd imagine a decent CPU will be required as well