If the auger is not turning you should first verify the motor is operating.
Kenmore ice maker auger not turning.
Infra red ligh read more.
Checked auger arm which turns when bin is empty but will not turn with ice in bin.
If the auger motor is defective pull out the ice bucket and turn the bucket auger by hand.
If the auger turns freely use a multimeter to test the auger motor for continuity.
Kenmore ice maker not working if the ice cubes have slowly begun to reduce in size and shape then the water flow has more than likely been restricted.
Ice maker works fine.
The motor gear box normally makes enough noise that you can hear it with the freezer door closed.
If the motor jumps slightly but fails to turn chances are the motor is frozen from moisture.
A kenmore ice maker that is not filling with water may have a frozen or clogged water line.
If the motor is not operating then you can check it for continuity with a multi meter.
Push on the ice dispensing lever as you watch the auger motor at the back of the freezer.