If my reading of the ACS712 datasheet is correct, the amount of variation you get due to the earth's magnetic field should be no greater than +/- 0.6/12 = +/- 0.05A. Is this what you observe? Is that an acceptable error?
To cancel most of the error, you could use 2 sensors close together in opposite orientations, and take the average of the two readings.
I found this application note on shielding: Redirect Notice.