Let $G$ be a simple graph with $n$ vertices and $m$ edges. Let edges of $G$ be given an arbitrary orientation, and let $Q$ be the vertex-edge incidence matrix of such oriented graph. The oriented incidence energy of $G$ is then the sum of singular values of $Q$. We show that for any $n\in N$, there exists a set of $n$ graphs with $O(n)$ vertices having equal oriented incidence energy.