Capacitors only store DC current.
Some capacitors are "rated" for use on AC supply voltages, but this rating has to do with the makeup of the dielectric (which insulates the two plates) used in the construction of the capacitor. The dielectric used for AC rated capacitors must be capable of rapid polarity changes over, and over again. The material used in DC rated capacitors does not have to do that. In any event, when a capacitor has been charged, it has a mass of positive electrons on one plate, and a large absence of electrons on the other plate, with the two plates separated by an insulating dielectric material. So, when you connect the capacitor to something, the electrons will seek to reach a state of equilibrium in a steady flow of current in one direction (which is direct current).
Some capacitors are large enough to produce dangerous shocks to humans if the terminals are accidently touched when the capacitor is fully charged. This situation may occur in capacitors rated for voltages higher than about 75 Volts DC. Very large capacitors rated at lower voltages than 75 Volts DC could also cause injury from burning skin or fingers
if the terminals are shorted and an arc is produced. So always use caution when dealing with high capacitance capacitors, especially when the combination of high voltage rating and high capacitance are involved.