Interacting selectively and non-covalently with a region of DNA that is a part of a type 3 promoter that controls transcription by RNA polymerase III. A type 3 Pol III promoter is composed of elements upstream of the transcription start site, including a TATA box. The human U6 snRNA gene has a type 3 promoter. Type 3 Pol III promoters have not been observed in S. cerevisiae.