As far as we’re aware at the Center for Legislative Archives, there is not a single, compiled list of all the unanimous votes cast by either the U.S. Senate or the U.S. House of Representatives.
However, there are several ways to find information on recorded votes online.
Congress.gov, the official website for U.S. federal legislative information, has links to roll call votes from the 101st Congress (1989) to today. Congress.gov also offers a resource guide on recorded votes.
If you’re looking for video, C-SPAN has made it easy to find votes by Congress.
There are also several resources available to locate voting records pre-1989. The first is GovTrack, which pulls data from a variety of published sources and has a section of their website dedicated to voting records. Another resource is Congressional Quarterly, a print publication likely available through a local library.
And there is always the Congressional Record -- the official record of debate and proceedings on the floor of the House and the Senate. The Congressional Record is published each day Congress is in session. The Congressional Record is freely available online through GovInfo. To find voting information, we recommend starting with the Index published at the end of each session. The predecessor publications to the Congressional Record are also available online through A Century of Lawmaking.
For more information on the congressional voting process, Parliamentarian’s of the House and Senate have written guides on the legislative process for each chamber -- see How Our Laws Are Made and Enactment of a Law.
Additionally, the Congressional Research Service (CRS) has published a number of reports on the legislative process. CRS reports are authoritative, objective, nonpartisan, and cover a wide range of topics. As an example, see the 2008 report: The Rise of Senate Unanimous Consent Agreements.