Yes, its usually the ice maker that is bad causing it not to fill with water, to verify that read below:
Pull the refrigerator out from the wall, then remove the lower access panel and locate the water inlet valve, where your water supply line hooks up to.
You'll need a multimeter to see if your getting 120 volts to the ice maker GREEN SOLENOID side of the water inlet valve. The GREEN SOLENOID is for the ice maker water. Just remove the plastic electrical connector that goes to it, then put your meter leads in each one and then cycle the ice maker(turn the gear 1/4 turn clockwise then let it rotate on its own) and watch your meter for 120 volts towards the end of the cycle for 5-7 seconds. If you don't get 120 volts for 5-7 seconds, then your ice maker is the culprit.