The level structure of $^{39}\mathrm{Ar}$ has been investigated via the stripping reaction $^{38}\mathrm{Ar}(d,p)^{39}\mathrm{Ar}$ at an incident deuteron energy of 10.064 MeV with an over-all experimental resolution of approximately 35 keV. Proton groups leading to 44 states of $^{39}\mathrm{Ar}$ with excitation energies up to 7.727 MeV have been identified. 30 of these states with excitation energies up to 6.488 MeV are neutron-bound. The orbital-angular-momentum-transfer values and the spectroscopic factors have been extracted for 28 of the observed neutron-bound states using zero-range distorted-wave Born-approximation (DWBA) calculations corrected for nonlocality of the optical potential and finite range in the local-energy approximation. One $l=0$, one $l=2$, twelve $l=3$, and fourteen $l=1$ transfer values are assigned. Spin assignments have been made on the basis of the conventional shell-model ordering of states, by comparison with the level structure of the isotonic nucleus $^{41}\mathrm{Ca}$ in the reaction $^{40}\mathrm{Ca}(d,p)^{41}\mathrm{Ca}$ and on the basis of the Lee-Schiffer effect. It is found that the conventional DWBA calculation with spin-orbit coupling reproduces the observed Lee-Schiffer effect for $l=1$ states remarkably well. The results of the present investigation are in fair agreement with those of recent shell-model calculations.