You will need more than one or two pins.
One of the switch's pins is the center pole (or common terminal or something like that, I'm not sure what the correct English term is). When you rotate the switch, it connects the center pole with one of the 12 other terminals. Connect the center pole to the Arduino's ground and the other terminals (as many of them as you need) to different digital input pins, for example pins 2 to 8. In you sketch, put the pins to the input-mode and enable the internal pull-up resistors. Associate the colors with different pins, for example 2=red, 3=green, ... 8=random. Read the pin values. The pin that is LOW is the one that is selected.