With Geocodio, you can upload a list of addresses or coordinates and receive the Congressional district information. Simply select "Congressional Districts" in Step 3 of the upload process.
You can download an example of the results when you add Congressional districts to a list of addresses here.
You can optionally receive contact and biographical information for each Senator and Representative. Select "Add legislator data" under "Congressional districts" in Step 3 of the upload process.
You can download an example of the results when you add Congressional districts and Congress contact information to a list of addresses here.