Back up first, of course. Place your cursor in the new State field and run Replace Field Contents by calculation. Calculation would be:
LeftWords ( Field ; WordCount ( Field ) - 1 )
Zip (which should be text) would be:
RightWords ( Field ; 1 )
... of course replacing Field with your actual field name which holds the full state/zip string.
NB: This wouldn't necessarily work for addresses outside of US (Canada, for instance, uses alpha-numeric zips). And I didn't assume that the state would be two-character either ... it will account if it is spelled out such as South Dakota (since you didn't specify the actual data). :^)