  Let $\mathbb{F}_q$ be a finite field of odd characteristic and
$2\nu+\delta\geq2$ an integer number with $\delta=0,1$ or $2$. The orthogonal
inner product graph $Oi\big(2\nu+\delta,q\big)$ over $\mathbb{F}_q$ is defined
and the automorphism groups of $Oi\big(2\nu+\delta,q\big)$ are determined. We
show that $Oi\big(2\nu+\delta,q\big)$ is a disconnected graph if
$2\nu+\delta=2$; otherwise it is not. Moreover, we have two necessary and
sufficient conditions for two vertices of $Oi\big(2\nu+\delta,q\big)$ and two
edges of $Oi\big(2\nu+\delta,q\big)$ respectively are in the same orbit under
the action of the automorphism group of $Oi\big(2\nu+\delta,q\big).$
