  We have measured the cross section of the $^{83}$Rb(p,$\gamma)^{84}$Sr
radiative capture reaction in inverse kinematics using a radioactive beam of
$^{83}$Rb at incident energies of 2.4 and $2.7 A$ MeV. Prior to the radioactive
beam measurement, the $^{84}$Kr(p,$\gamma)^{85}$Rb radiative capture reaction
was measured in inverse kinematics using a stable beam of $^{84}$Kr at an
incident energy of $2.7 A$ MeV. The effective relative kinetic energies of
these measurements lie within the relevant energy window for the $\gamma$
process in supernovae. The central values of the measured partial cross
sections of both reactions were found to be $0.17-0.42$ times the predictions
of statistical model calculations. Assuming the predicted cross section at
other energies is reduced by the same factor leads to a slightly higher
calculated abundance of the $p$ nucleus $^{84}$Sr, caused by the reduced rate
of the $^{84}$Sr($\gamma$,p)$^{83}$Rb reaction derived from the present
measurement.
