  We introduce the Exel-Pardo $*$-algebra $\mathrm{EP}_R(G,\Lambda)$ associated
to a self-similar $k$-graph $(G,\Lambda,\varphi)$. We prove the
$\mathbb{Z}^k$-graded and Cuntz-Krieger uniqueness theorems for such algebras
and investigate their ideal structure. In particular, we modify the graded
uniqueness theorem for self-similar 1-graphs, and then apply it to present
$\mathrm{EP}_R(G,\Lambda)$ as a Steinberg algebra and to study the ideal
structure.
