  Assume that $\nu$ is a positive integer and $\delta=0, 1$ or $2$. In this
paper we introduce the orthogonal graph $\Gamma^{2\nu+\delta}$ over a Galois
ring of odd characteristic and prove that it is arc transitive. Moreover, we
compute its parameters as a quasi-strongly regular graph. In particular, we
show that $\Gamma^{2+\delta}$ is a strongly regular graph and $\Gamma^{2\nu+1}$
is a strictly Deza graph when $\nu\geq 2$.
