I have looked into http://wiki.roblox.com/index.php?title=Mobile_Controls only to get information on how to add new buttons or information about how to use the touchscreen instead of anything on the joystick that Roblox provides to move the character.
Is there any way to hook a script onto the joystick that moves your character to tell a script that the user moved it up, down, left, right, or let their finger off?

2 comments
Not a physical joystick.. The joystick you use to move your character around ingame on a mobile device like an android or apple phone.
You're talking about the Thumstick? I'm not sure if you can check.