The Decennial Census is mandated by the Constitution and the data collected are used to determine the number of seats each state has in the U.S. House of Representatives. After the apportionment of congressional seats among the states based on decennial census population counts, each state is responsible for establishing congressional districts for the purpose of electing representatives. Thus Census data is retabulated by congressional districts only after the districts are established by states.
The Census Bureau published Congressional Data Books in recent decades starting with the 1960 Census where you can find population and housing data tabulated by congressional districts. There are other efforts by academic and research institutions to retroactively aggregate county-level data into congressional districts for prior decades. Current data for congressional districts are readily available from the Census Bureau in a user-friendly format.
While most of the resources come from the U.S. Census Bureau there are some government agencies that present their data by congressional districts that are included here. Also included are geographic information sources such as atlases, maps, and digital shape files. Some of the geographic information sources are available in the Geography and Map Reading Room.