You can buy servos with the pot output broken out. Adafruit sells some. You would read the pot with analogRead(), though. With a regular unmodified servo, there is no way to measure the position of the servo without adding a feedback mechanism (pot, rotary encoder,...)
Edit: a search of the net will yield instrctions on how to modify a servo to break out the pot signal. Be careful how the servo is powered. The output voltage of the pot will be, at max, the servo supply voltage. If that voltage is more than the Vcc of the Arduino, the Arduino can be damaged.