It sounds like your servo is drawing more power than the Arduino can supply. You probably need to wire the servo motor to a separate power supply, and just have the control come from the Arduino. Be sure to connect the grounds of the two power supplies. DuaneB wrote a tutorial on how to wire up servos: http://rcarduino.blogspot.com/2012/04/servo-problems-with-arduino-part-1.html
Note, that you will not be able to use pins 9 and 10 for PWM functionality for other items on an UNO with a servo. I ran into this when I tried to use an LCD shield (which wanted to use those pins) and a servo.