I have seen stepper switches which are solenoid-controlled rotary switches. You pulse the solenoid for a specified time at a specified voltage, and the switch advances to the next position. However, such things are physically large, not easily and commonly available, and quite expensive.
The right solution is to step back two logical layers and define what you really want to accomplish, and leave any supposed solution like a rotary switch out of it.
Apparently you want to switch 100 V at 10 mA to 6 different feeds. That should be doable using transistors for much lower cost, much lower size, and much higher reliability. To recommend the best architecture, you need to tell us more about what is being switched on and off. For example, is it OK to switch the grounds, or must the power be switched?
At worst, a few FETs or BJTs as high side switches should work here. These can be controlled from a microcontroller, which can implement the sequencing logic to emulate a rotary switch, if that even matters. Basically, the micro has individual control over each of the 6 switches, and the rest is firmare logic.
I see using relays is a popular answer. That would certainly work, but relays have downsides too. The way to decide whether relays or transistors are more appropriate is whether you need isolation or not, which you haven't told us. If you need isolation between these power feeds that are being switched and the control logic that decides what needs to be switched when, then I'd use relays. If everything has a common ground then I'd use transistors.
Transistors will be smaller, cheaper, and last much longer than relays, so I'd use the relays only if the the extra isolation they provide was a benefit.