  Let $G$ be a simple graph with an orientation $\sigma$, which assigns to each
edge a direction so that $G^\sigma$ becomes a directed graph. $G$ is said to be
the underlying graph of the directed graph $G^\sigma$. In this paper, we define
a weighted skew adjacency matrix with Rand\'c weight, the skew Randi\'c matrix
${\bf R_S}(G^\sigma)$, of $G^\sigma$ as the real skew symmetric matrix
$[(r_s)_{ij}]$ where $(r_s)_{ij} = (d_id_j)^{-\frac{1}{2}}$ and $(r_s)_{ji} =
-(d_id_j)^{-\frac{1}{2}}$ if $v_i \rightarrow v_j$ is an arc of $G^\sigma$,
otherwise $(r_s)_{ij} = (r_s)_{ji} = 0$. We derive some properties of the skew
Randi\'c energy of an oriented graph. Most properties are similar to those for
the skew energy of oriented graphs. But, surprisingly, the extremal oriented
graphs with maximum or minimum skew Randi\'c energy are completely different.
