  The periapsis shift of charged test particles in arbitrary static and
spherically symmetric charged spacetimes are studied. Two perturbative methods,
the near-circular approximation and post-Newtonian methods, are developed, and
shown to be very accurate when the results are found to high orders. The former
method is more precise when the eccentricity $e$ of the orbit is small while
the latter works better when the orbit semilatus rectum $p$ is large. Results
from these two methods are shown to agree with each other when both $e$ is
small and $p$ is large. These results are then applied to the
Reissner-Nordstr\"om spacetime, the Einstein-Maxwell-dilation gravity and a
charged wormhole spacetime. The effects of various parameters on the periapsis
shift, especially that of the electrostatic interaction, are carefully studied.
The periapsis shift data of the solar-Mercury is then used to constrain the
charges of the Sun and Mercury, and the data of the Sgr A$^*$-S2 periapsis
shift is used to find, for the first time using this method, constraints about
the charges of Sgr A$^*$ and S2.
