As others have stated, the question is not so clear.
However I will hazard a guess. My guess is you want to perhaps use the switches of whatever from the controller you included a photo of to interface with your arduino.
The answer is of course you can. However as was mentioned, you must know what the part you are trying to use does. A switch or potentiometer is simple to understand. Other parts may not be.
You should also understand many of the folks here who answer these questions have boxes of unused parts so for them it might not be worth the effort. For someone starting out seeing and touching an assembly of any sort is a learning experience.
BTW from the photo I have no clue what the item is. I see what looks like a joystick but that's all I can tell.