The servo has 3 Pins to connect: Vcc, GND and PWM. The power, which actually drives the servo is drawn through the power lines Vcc and GND. The PWM pin, which is connected to an Arduino output pin, does not draw mich current. It is only for the PWM (-like pulsed) signal, which tells the servos driver, which angle is requested. But you should not power the servo through the Arduino. You have to connect it directly to a power supply with the correct voltage, because some parts of the Arduino can get fried, when drawing too much current through it.
So all in all: Connect the PWM pin directly to an Arduino output pin and supply the power from the source directly to the servo, not going through the Arduino.