  If the graviton possesses a non-zero charge $q_g$, gravitational waves (GW)
originating from astrophysical sources would experience an additional time
delay due to intergalactic magnetic fields. This would result in a modification
of the phase evolution of the observed GW signal similar to the effect induced
by a massive graviton. As a result, we can reinterpret the most recent upper
limits on the graviton's mass as constraints on the joint mass-charge parameter
space, finding $|q_g|/{e} < 3\times 10^{-34}$ where $e$ represents the charge
of an electron. Additionally, we illustrate that a charged graviton would
introduce a constant phase difference in the gravitational waves detected by
two spatially separated GW detectors due to the Aharonov-Bohm effect. Using the
non-observation of such a phase difference for the GW event GW190814, we
establish a mass-independent constraint $|q_g|/e < 2\times 10^{-26}$. To the
best of our knowledge, our results constitute the first-ever bounds on the
charge of the graviton. We also discuss various caveats involved in our
measurements and prospects for strengthening these bounds with future GW
observations.
