Rudolf Kuntz received painting and drawing lessons from his father, the painter Carl Kuntz. He first attracted attention in 1820 with drawings and etchings of views of the Rhine, Neckar and Moselle, which were published in a collection by the Heidelberg publisher Joseph Engelmann. In 1823, Kuntz was commissioned by the Württemberg stud directorate to illustrate royal Württemberg stud horses, which were published in three booklets in 1824. This was followed in 1827/32 by "Abbildungen sämmtlicher Pferderaçen" in four volumes, published by the Karlsruhe art dealer Johann Velten, for which the art critic Joseph Eduard d'Alton wrote the explanatory text. This work was preceded by study trips to Hungary, London and Paris, where Kuntz painted the various breed horses in their natural environment.

After the death of his father in 1830, Kuntz acted temporarily as director of the picture gallery. In March 1832, he was appointed court painter by Grand Duke Leopold. This came with the obligation to donate a painting to the gallery every two years.

Kuntz's oeuvre consists mainly of landscape paintings, in which horses, and occasionally other animals such as storks, sheep and cows, can be seen. The dining room of Stutensee Palace near Karlsruhe contains a cycle of twelve paintings of English stud horses painted by Kuntz. Kuntz died at the age of 50 in "mental derangement" in the Illenau sanatorium and nursing home.