Google has a number of public datasets in BigQuery including geographic boundries based on census data.
Currently I have only 1 query to find intersection of zip codes with congressional districts. Will add more queries as I write them.
Go to https://console.cloud.google.com/bigquery and click Add Data in the left-hand console
Once you add the public datasets, BigQuery should allow you to query them
zip_cd.sql - Finds congressional district that intersects with a given zip code
cd_geo_id - The census has a geo_id for everything. You can find more information on that here. In the case of congressional districts it is a 4 digit number. The first 2 represent the state number which is the state's alphabetic position. For example, Texas is 48. The second 2 numbers represent the congressional district. So 4801 is the id for Texas's First Congressional district
lsad_name - Name of congressional district (i.e 8th Congressional District)
lsad_code - More details here
district_fips_code - Number of the congresional district (Note: at-large districts are labeled 00)