You'd need to check the voltage into the ADC on a multimeter (or scope) that's in known calibration and compare that with the data the ADC is giving you simultaniously. Or feed it a fixed voltage from a known calibrated reference. The DAC is going to introduce it's own error, so you're not directly measuring the ADC's error unless the DAC itself is in known calibration, which requires approximatly the same steps as calibrating the ADC itself so is a bit silly =)
The equation for calculating SNR can be found here, and would be at the ADC without the DAC, again unless the DAC is in known calibration, otherwise you're calculating the total error of the ADC and the DAC together, not just the ADC.
Signal-to-noise ratio - Wikipedia, the free encyclopedia