Yes.
According to Andrew Carnie (Syntax, a Generative Introduction; third edition), that's a determiner phrase, apparently because it starts with a determiner.
Carnie explains that in modern x-bar theories, a sentence is presented as TP which includes a DP and a VP under a V' node. And sometimes a CP is needed under a VP, like when you say "My mother said that he helped people a lot". Here "my mother" is a DP. "that he helped…" is a CP.
By the way, my question is how to draw a tree for "the paw of the kitten"?