A rectifier will only make things worse. At best, you're trading an ill-defined offset voltage for a combination of input offset error plus saturation error.
So, what to do?
Simple: measure the ill-defined offset voltage, then measure the offset-ed signal. Subtract (or use a "differential" ADC or input mode -- but these are either extra hardware or poor performing) and you have your answer.
If you have many signals, you only need to measure the offset once per set; an example I've used before is reading three phase AC line current transformers. All three have one side biased to VCC/2 (which goes to ADC0), the other side (with suitable burden resistor attached) to ADC1, 2 and 3. Read all four during each sample interval, and subtract: give or take a few microseconds or so, there lies your answer(s).
Tim