Can an electric current be created within a closed loop of wire using an electric field? I would like to know if a small electric current can be created in a closed loop of wire by using a strong electric field to move the free electrons within the closed loop of wire.
To create this strong electric field, a high voltage DC power supply could be used, one that say generates 100 kV. The power supply's two electrodes will need to be covered with insulation, such as mica, so no electric current can flow between them, yet the mica will allow the electrodes' electric charges to pass through them.
I believe that in order for the free electrons on the outer surface of the wire to be moved, the section of wire between the two electrodes cannot have any wire insulation around it. Also, the wire's insulation will need to be a material with a very high dielectric constant. I think an ideal material to use could be calcium copper titanate, which has a dielectric constant/relative permittivity of >250,000 (per Wikipedia). I am not sure if this material can completely block an electric charge of 100 kV for I have never worked with this material before.
To illustrate how this would work, I have created the following drawing. (This drawing is showing a cross-sectional view and the two electrodes have holes in the middle of them with the wire passing through them.)

I believe that the free electrons on the outer surface of the wire will be moved towards the positive electrode and they will want to stay close to it, but they will be pushed pass this electrode due to the continuous flow of other free electrons being sent forward by the repulsion force coming from the negative electrode. The result should be that there should be a flow of free electrons moving in the closed loop of wire which should create a small electric current.
Can an electric current be created within a closed loop of wire using an electric field?
 A: Electric fields are conservative.  Any shape you create with electrodes or insulators or dieletrics is irrelevant.  A closed loop through any such static field will sum to zero potential change.  So no current is created.
Your field may in fact create a strong push on charges in the section between the electrodes, but the rest of the loop will feel the exact same push in the opposite direction.
You would need to have a varying electric field to establish a current in a regular conductor.

If the layer of calcium copper titanate within the wire sheath can completely block the electrical charge emanating out from the two electrodes, then there shouldn't be any electrostatic push in the opposite direction on the free electrons that reside outside of the electric field.

Sorry, that's not possible.  How do we modify electric fields?  By using charged particles.  Using conductors with mobile charges inside can exclude fields from inside a cavity.  But the arrangement of charges that excludes the field inside the location you want also creates a stronger field outside.  A loop path still sums to zero.
The main problem here is that you cannot get rid of "edge effects".  The area between the electrodes may have a fairly uniform field, and the insulated wire may have a nearly zero field.  But by doing so, you will create very strong fields at the boundary between them.  Those fields at the boundary will be exactly sufficient to counter the field between the electrodes.
See also: Conservative forces in wikipedia.
