Can neurons be inhibited with electric current?
Yes, but maybe not how you think.

It is important to recognize that voltages refer to potential differences. When we say the "a cell is at -65mV" for example, we mean "The potential difference across the cell's membrane to the extracellular space is -65mV." When you stimulate electrically, you create a transient electric field, whereby the extracellular space is no longer effectively isopotential.

Let's imagine for the sake of some neuron that this field strength is on the order of 40 mV across the membrane. If this electric field is perpendicular to some neuronal process, the voltage across the membrane will be about -105mV on one side, and -25mV on the other side. The -25mV side is now depolarized enough to open voltage gated sodium channels, and some current is flowing into the cell. Once the shock has passed, positive current will continue to flow through those open channels and open more channels. It doesn't matter much that the other side is transiently at -105mV, all that matters is that you opened a bunch of voltage gated sodium channels which starts a positive feedback loop.

Therefore, transient electrical simulation will almost always be excitatory. There are two exceptions:

1) Neurochemical inhibition. If you excite a particular brain region that is specifically inhabited by inhibitory projection neurons, you will primarily excite those inhibitory cells and therefore cause excitation elsewhere. Of course, in this case, the electrical stimulation itself is still directly exciting cells, they just happen to have inhibitory effects elsewhere.

2) Depolarization block. If you continually stimulate the same population of neurons with a high-frequency stimulation, you can put neurons in a state called "depolarization block." Voltage-gated sodium channels have a chance to inactivate whenever they are activated. If you inactivate enough channels, there aren't enough available to produce an action potential. Therefore, if you can keep a cell pretty much constantly depolarized by continually stimulating, you can prevent action potential propagation because too many of the voltage gated channels in the axon initial segment are inactivated.