How to digitize an AC signal?
I need an accuracy of 0.1% in the digital signal.


An 8 bit ADC has a resolution of 1 in 256 = 0.39% therefore you need to choose an ADC that is at least 10 bit (0.097% resolution). But resolution isn't accuracy and accuracy can't be achieved without a greater resolution so you need to start digging into the specifications of an ADC that might suit your needs.

You need to consider INL, DNL, offsets, gain-errors and noise to be confident about predicting accuracy. INL stands for integral non-linearity and here's a picture to help you understand: -



Basically it's a curvature problem and below here's DNL (differential non-linearity): -



Offset problems: -



Gain error: -



Pretty pictures stolen from here


  Do I need to apply an offset first?


If it's an AC signal then you'll likely need to apply a DC offset to position the centre-line of the AC signal to the mid-point of the ADC input range.


  How is the process different than that for DC?


It's no different - a slow moving DC value should be treated in the same way as a repetitive AC signal.