Yes, we do, with some gaps in our holdings. From the Catalog - University of Arkansas record (linked below), you can see the various holdings we have for the catalogs going back to 1872. 

More recent catalogs (1995/96 - ) are found online (linked below).

Special Collections and Digital Services Unit digitized older editions of the Catalog of Studies, fifty-two catalogs ranging from 1872 through 1925 (linked below).

Other pre-1995 catalogs can be requested from the Library Annex.