Does looking at this https://en.wikipedia.org/wiki/Reissner–Nordström_metric , suggest that charge does in fact dilate time?
For this metric charge is a component of the total mass. Charge per unit mass. So when charge is maximal the total mass would be 2 solar mass for a solar mass Schwarzschild black hole. If the charge per unit mass is 0 then the metric for that spacetime is the spherically symmetric non rotating uncharged Schwarzschild metric. To determine any difference in tick rate two local proper frames need to be compared. Two things that effect the tick rate are gravitational time dilation and time dilation due to relative velocity. So the extra mass associated with charge is a component of the local gravitational time dilation.
A more direct response to the OP (without resorting to black holes) is possible. Strictly speaking, the answer would be "no" because electric charge is something static (something which does not move). However, there is this: http://physics.stackexchange.com/questions/100279/does-strong-magnetic-field-cause-time-dilation And I would agree with the best answer given, bur for a more physical reason. Matter, whether it is paramagnetic, ferromagnetic, or diamagnetic, will all respond to an externally applied magnetic field that is the result of moving electric charges. Strong magnetic fields produce eddy currents in all of the above, which according to Lenz's law, will result in induced loops of electric currents which work to counteract the effects of externally applied magnetic fields, but in all cases, electrons within the structure of matter will move in accordance with the electrical, magnetic and chemical processes their structures will support. Applying an external magnetic field to matter is therefore a means of inducing it to move without actually moving it. The moving electrons in the opposing induced currents will experience a time dilation effect that is not the same as the same chunk of mass in the absence of externally applied magnetic fields. However the question of whether electrostatic fields (which come in positive and negative charges) induce time dilation directly is still an open one that will be difficult to answer because it would seem to be impossible to aggregate a large amount of the same polarity of electrical charge in the same region of space without it flying apart. Nature's most direct and best answer therefore would be: "this never happens", at least, in the universe we inhabit in this epoch.
