The Census geographic hierarchy diagram indicates that Congressional Districts are built from Census Blocks. However, I don't see any crosswalks from blocks to congressional districts on the Census Congressional District Relationship Files website section. I also couldn't find such a crosswalk on sites like NHGIS, though I did just ask on the IPUMS forum.
A similar question was asked in 2015, but it asked about a specific past congressional session, and all the links in questions and answers are now dead.
Specifically I'm most interested in a crosswalk from 2010 Census Block to 117th (current) Congressional District, but ideally would like to know a general solution.