The data exists but it is unlikely to be open. From the U.S. Census Bureau (recall there is a crosswalk between SIC and NAICS codes)
Can I get a NAICS code or other statistical data for a specific company?
Title 13, U.S. Code, Section 9 (a) prohibits the U.S. Census
Bureau from releasing information on a specific business including
I found it here: https://www.dnb.com/utility-pages/dnb-demographic-firmographic-code-tables.html:
There are 2,4,6,8-digit SIC, Local Activity Type, and NAICS.
Here is a link to a dataset of businesses from Paducah, KY, which include a SIC designation.
I'm not exactly sure what's going on with these industry codes. I looked into it briefly and since it's a six-digit code I'm wondering if it's not reflecting the NAICS 2017 revision or some other weird industry code. I didn't name the columns so I'm not sure what ...