  Ground state properties of proton-rich odd-$Z$ nuclei in the region $55\le Z
\le 73$ are studied in the relativistic mean field (RMF) theory. The RMF
equations are solved by using the expansion method in the Harmonic-Oscillator
basis. In the particle-particle channel, we use the state-dependent BCS method
with a zero-range $\delta$-force, which has been proved to be effective even
for neutron-rich nuclei. All the ground state properties, including the
one-proton separation energies, the ground state deformations, the last
occupied proton orbits and the locations of proton drip line, are calculated.
Good agreement with both the available experimental data and the predictions of
the RHB method are obtained.
