22mV/A * 0.3A = 6.6mV
So your 0.3A RMS AC current will produce a 6.6mV RMS AC voltage at your ADC input. It is a 12-bit ADC. So if the ADC reference is 5V, then the resolution of the ADC is:
5/(2^12-1) which is 5/4095 = 1.22mV
So you will be trying to measure a 6.6mV (rms) signal with a 1.22mV resolution ADC. In practice this will not work super well. The current error, when you include all sources of error, will probably be pretty large. A 0.3A AC current may be detectable, but you will be unable to distinguish between a 0.3A current and a 0.4A current or 0.2A.
Using a lower reference voltage may help. There is another potential problem in that you have to make sure the output of the sensor is in the allowable range of the ADC inputs. If the ADC can measure 0-5V, then you need to make sure the sensor is always between 0 and 5V. If the ADC can only measure 2.5V, then you need to make sure your signal is always under 2.5. Etc.