I found a rotary switch on an Arduino ready board. It uses a resistor ladder/voltage divider driven by 5V with the output going to an analog input on the Arduino. This one also has an LED on each position.
It is DFRobot Analog Rotary Switch Module V1. It is $5.40 at https://www.dfrobot.com/product-970.html The site also has a schematic and code.