Transforming ArcGIS date field to integer?

I suggest that you use strftime('%Y%m%d') in the field claculator.

Just for the sake of completeness, your method is not very "pythonic" but it seems correct. However,the wrapping of your python code block as shown on your post looks incorrect. Unlike with VB, you need to define a fucntion in the code block, and call it in the field calculator.

code_block_function(!ACQ_DATE!)

in the code block, use:

def code_block_function(a):
    date=str(a)
    year= date.split("-")[2]
    month= date.split("-")[1]
    day= date.split("-")[0]
    dateInt= int(year) * 10000 + int(month) * 100 + int(day)
    return dateInt