It’s certainly simple to do but it’s pretty hacky - you need move the mouse with the joystick since i believe only the mouse will interface with the Mouse actuator when set to Look. You can do this with just an always sensor, python controller with a small script(5 lines), and a mouse look actuator. The problem with this is that any actual mouse movement(the one connected to your computer) will also activate the mouse look actuator.
Even though I don’t recommend using this method or possibly any another method someone may suggest that involves connecting the joystick to a mouse look actuator, I’ll leave the code here so you can decide for yourself.
from bge import logic
cont = logic.getCurrentController()
joy1 = logic.joysticks
logic.mouse.position = logic.mouse.position + joy1.axisValues * 0.05, logic.mouse.position + joy1.axisValues * 0.05
The reason I recommend using a different approach is because you can easily achieve the same result as a mouse look actuator with a little more python code(to rotate the object and to simulate the sensitivity and threshold functionality). Or you could connect 4 joystick sensors to 4 motion actuators and do without some of the extra stuff.
If python is the stumbling block for you, I recommend you start learning it. It really isn’t a difficult language. Your game designs will get exponentially better.