  The randomly oriented graph $G_{n,p}^{\sigma}$ is an Erd\H{o}s-R\'enyi random
graph $G_{n,p}$ with a random orientation $\sigma$, which assigns to each edge
a direction so that $G_{n,p}^{\sigma}$ becomes a directed graph. Denote by
$S_n$ the skew-adjacency matrix of $G_{n,p}^{\sigma}$. Under some mild
assumptions, it is proved in this paper that, the spectral distribution of
$S_n$ (under some normalization) converges to the standard semicircular law
almost surely as $n\rightarrow\infty$. It is worth mentioning that our result
does not require finite moments of the entries of the underlying random matrix.
