  In this paper, we prove the local well-posedness of the Yang-Mills system in
the Lorenz gauge for initial data in the Besov space $B^\frac12_{2,1}\times
B^{-\frac12}_{2,1}$ with additional angular regularity. To the best of our
knowledge, our study is the first result on $(1+3)$ dimensional Yang-Mills
system with initial data in the scaling critical regularity.
