An ADC measures an analogue voltage a DAC generates one.
Since it measures voltage you have to convert the current into a voltage.
The normal way to do this, eg in a digital multimeter - is to connect a small resistor in series and measure the voltage across the resistor, then use ohm's law to calculate the current. With AC it's a little more complicated - you will have to measure the voltage at many points in the AC cycle and calculate the RMS.
What sort of current / voltage are you looking at?
If you are doing this with very high currents (eg car battery) or high voltages (eg household wiring) you probably want to learn a little more before you try.