Why does engine rev high on its own when air conditioner is on? on 1990 Mazda Miata MX-5

This happens every time I turn on the air with the fan on. The car has over 168,000 miles. Please help because it is extremley hot here, 120 degs. in Lake Havasu, Az.

Asked by for the 1990 Mazda Miata MX-5