Catalysis of the reaction: adenosine 3',5'-diphosphate + H(+) + sulfite + thioredoxin disulfide = 3'-phospho-5'-adenylyl sulfate + thioredoxin. Thioredoxin disulfide is the oxidized form of thioredoxin; 3'-phosphoadenosine 5'-phosphosulfate is also known as PAPS.