  Nuclear single-proton resonances are sensitive to the Coulomb field, while
the exchange term of Coulomb field is usually neglected due to its nonlocality.
By combining the complex scaling method with the relativistic mean-field model,
the influence of the Coulomb exchange term on the single-proton resonances is
investigated by taking Sn isotopes and $N=82$ isotones as examples. It is found
that the Coulomb exchange term reduces the single-proton resonance energy
within the range of $0.4-0.6$ MeV, and lead to similar isotopic and isotonic
trends of the resonance energy as those without the Coulomb exchange term.
Moreover, the single-proton resonance width is also reduced by the Coulomb
exchange term, whose influence generally decreases with the increasing neutron
number and increases with the increasing proton number. However, the influence
of the Coulomb exchange term cannot change the trend of the resonance width
with respect to the neutron number and proton number. Furthermore, the
influence of the Coulomb exchange term on the resonance width is investigated
for the doubly magic nuclei $^{40}$Ca, $^{56,78}$Ni, $^{100,132}$Sn, and
$^{208}$Pb. It is found that the Coulomb exchange term reduces the proton
resonance width within $0.2$ MeV, whose magnitude depends on the specific
nucleus and the quantum numbers of resonant states.
