This CSV uses the
census_geo_containment table of CensusReporter's TIGER dumps to show the relationship between zipcodes (represented here as ZCTAs) and counties. It's important to note that ZCTAs are not zipcodes. Further, the ZCTA dataset haven't been updated since 2010, and are out of date. But this is a pretty good place to start and is still useful.
Geographies are represented here using extended Census geoids. If you chop off the first 7 characters of the
child_zip values you'll get the zipcode and if you chop off the first 7 characters of the
parent_county you'll get the county's FIPS code. For quick debugging, you can pass these geoids into CensusReporter URLs like so:
https://censusreporter.org/profiles/<geoid> (e.g. https://censusreporter.org/profiles/05000US72099).