how to connect PS Vita analog stick to Leonardo

Hi all,

I'm having to temporarily retire from league of legends due to repetitive stress injuries Resulting from long-term use of off-the-shelf products such as razor orb weaver, keyboards, mouses, trackballs, etc.. In order to return to league, I have determined that I must build a custom gaming controller.

I would be grateful for the Arduino community's assistance on this project.

To begin with, can someone tell me if it is possible to connect this PlayStation Vita analog stick to a Leonardo board?

The analog stick can be seen here: