A graceful difference labeling (gdl for short) of a directed graph $G$ with vertex set $V$ is a bijection $f:V\rightarrow\{1,\ldots,\vert V\vert\}$ such that, when each arc $uv$ is assigned the difference label $f(v)-f(u)$, the resulting arc labels are distinct. We conjecture that all disjoint unions of circuits have a gdl, except in two particular cases. We prove partial results which support this conjecture.