Can capacitor store charge from ac source?

Yes. A capacitor stores charge from any source, including AC.

The difference between DC and AC, however, is that the capacitor will be constantly changing in charge, in step with the AC. Due to the nature of the capacitor, the current through the capacitor will lead the voltage by some amount, depending on capacitance and resistance. {In the ideal case of a perfect capacitor, conductors, and AC power source, the current will lead the voltage by 90 degrees phase angle.}

This is called capacitive reactance.

Another way for a capacitor to store charge from an AC source, of course, is to place a rectifier diode in front of the capacitor. This, then, becomes an AC to DC converter.