Catalyzes the formation of sulfite from adenosine 5'-phosphosulfate (APS) using thioredoxin as an electron donor. [thioredoxin]-disulfide + AMP + 2 H(+) + sulfite = [thioredoxin]-dithiol + adenosine 5'-phosphosulfate Binds 1 [4Fe-4S] cluster per subunit (PubMed:11940598, PubMed:15491155, PubMed:16289027, PubMed:17010373). The cluster is required for activity and may play a role in binding and activating the substrate for thiol-mediated reduction (PubMed:15491155, PubMed:16289027, PubMed:17010373). Optimum pH is 8.5. Sulfur metabolism; hydrogen sulfide biosynthesis; sulfite from sulfate. Homotetramer. The two chemically discrete steps of the overall reaction take place at distinct sites on the enzyme, mediated via conformational flexibility of the C-terminal 18 residues. Cysteine auxotrophy. Belongs to the PAPS reductase family. CysH subfamily. The [4Fe-4S] cluster was originally thought to be ligated by three cysteine residues, but the crystal structure establishes that it is ligated by four cysteine residues.