  The purpose of this paper is to study the cyclic self orthogonal codes over
$\mathbb{Z}_{p^m}$. After providing the generator polynomial of cyclic self
orthogonal codes over $\mathbb{Z}_{p^m}$, we give the necessary and sufficient
condition for the existence of non-trivial self orthogonal codes over
$\mathbb{Z}_{p^m}$ . We have also provided the number of such codes of length
$n$ over $\mathbb{Z}_{p^m}$ for any $ (p,n) = 1 $.
