I would like to use this US deprivation index (https://www.neighborhoodatlas.medicine.wisc.edu), which is based on Census Block Groups. Where can I find the corresponding shapefiles?
Based on their FAQ https://www.neighborhoodatlas.medicine.wisc.edu/ it looks like they are using 2009-2013 American Community Survey data. In which case, it is best to use the 2013 version of the block group shapefiles from the US Census Bureau, per https://www2.census.gov/geo/pdfs/maps-data/data/tiger/How_do_I_choose_TIGER_vintage.pdf
For ACS data, use the TIGER products for the last year in the range for the ACS estimates. For example, if using ACS 2007-11 estimates, use 2011 TIGER products.**
You can read their (Singh GK or Kind AJH, Jencks S, Brock J, et al.) methodology papers for additional details as to how the US Deprivation Index was created.
You can download the Block Groups (note there's also an option to download via FTP) from https://www.census.gov/geo/maps-data/data/tiger-line.html. Select the year and geography type.
The Neighborhood Atlas site also has a download section which requires registration. It is possible that they offer shapefile downloads of their results.