  We consider random $n\times n$ matrices of the form
$Y_n=\frac1{\sqrt{d}}A_n\circ X_n$, where $A_n$ is the adjacency matrix of a
uniform random $d$-regular directed graph on $n$ vertices, with $d=\lfloor p
n\rfloor$ for some fixed $p \in (0,1)$, and $X_n$ is an $n\times n$ matrix of
iid centered random variables with unit variance and finite $4+\eta$-th moment
(here $\circ$ denotes the matrix Hadamard product). We show that as $n\to
\infty$, the empirical spectral distribution of $Y_n$ converges weakly in
probability to the normalized Lebesgue measure on the unit disk.
