  This article studies the \emph{$k$-forcing number} for oriented graphs,
generalizing both the \emph{zero forcing number} for directed graphs and the
$k$-forcing number for simple graphs. In particular, given a simple graph $G$,
we introduce the maximum (minimum) oriented $k$-forcing number, denoted
$\MOF_k(G)$ ($\mof_k(G)$), which is the largest (smallest) $k$-forcing number
among all possible orientations of $G$. These new ideas are compared to known
graph invariants and it is shown that, among other things, $\mof(G)$ equals the
path covering number of $G$ while $\MOF_k(G)$ is greater than or equal to the
independence number of $G$ -- with equality holding if $G$ is a tree or if $k$
is at least the maximum degree of $G$. Along the way, we also show that many
recent results about $k$-forcing number can be modified for oriented graphs.
