Both alternating current and direct current are measured in amperes. But how is the ampere defined for an alternating current?

For AC circuit RMS value is used. As current changes direction in AC circuits. RMS value averages both the negative and positive parts. Also, heat produced due to direct current through a device and heat due to AC current through the same device would be same. Thus, Joules heating effect is used to defines RMS value of the AC current.