A linear $k$-diforest is a directed forest in which every connected component is a directed path of length at most $k$. The linear $k$-arboricity of a digraph $D$ is the minimum number of linear $k$-diforests needed to partition the arcs of $D$. In this paper, we study the linear $k$-arboricity for digraphs, and determine the linear $3$-arboricity and linear $2$-arboricity for symmetric complete digraphs and symmetric complete bipartite digraphs.