ACS712 Not working correctly with Arduino
You are seeing that because that is what the current is doing. It's called AC - Alternating Current. It's what the mains current is.

To work with AC you have to rapidly sample over a short period to get the maximum and minimum values. Subtract one from the other and that gives you the peak-to-peak current. You can then use that to calculate the RMS current which is what you are (most likely) interested in.


http://whatis.techtarget.com/definition/root-mean-square-RMS