Is there a DNA analogue to ribozymes?
Not very common, and not found so far in nature, but they exist and are called deoxyribozymes.

Additional information:

Deoxyribozymes are the equivalent of ribozymes in the DNA world and can function as catalysts for different biochemical reactions, such as DNA cleavage. While DNAzymes (short name) were synthesized in a laboratory context (In-vitro) and proved to be active, no observations were made of DNA molecules having an enzymatic activity In-vivo which is of course not a definitive proof they don't exist in nature. 

The latter point is a major difference compared to ribozymes which were proved to be active and functional in living cells.