  Motivated by the conjecture of Hartsfield and Ringel on antimagic labelings
of undirected graphs, Hefetz, M\"{u}tze, and Schwartz initiated the study of
antimagic labelings of digraphs in 2010. Very recently, it has been conjectured
in [Antimagic orientation of even regular graphs, J. Graph Theory, 90 (2019),
46-53.] that every graph admits an antimagtic orientation, which is a
strengthening of an earlier conjecture of Hefetz, M\"{u}tze and Schwartz. In
this paper, we prove that every $2d$-regular graph (not necessarily connected)
admits an antimagic orientation, where $d\ge2$. Together with known results,
our main result implies that the above-mentioned conjecture is true for all
regular graphs.
