I am working on dielectric elastomer actuator which just like the variable capacitor. To charge this we need high voltage fro 5 to 10 kV. I charge this capacitor to this voltage and want to measure leakage current of the capacitor. How can I measure the leakage current of this capacitor? Is there any electrical circuit that I have to build or there any instrument for that?
It sounds like you know the current (800uA when 8kV is applied).
It's possible (with a great deal of care) to simply put a milliammeter in series with the capacitor. You should put it in series with the grounded side of the supply so that the meter leads are at approximately ground potential and make sure that connection is reliable. While 800uA is probably not enough to cause injury, it would not be nice. Contact with your supply (the ungrounded side) could result in much higher (possibly fatal) current.
Note that at 8kV you may be getting corona discharge (especially if you have pointy bits facing a strong electric field gradient). This behaves similarly to leakage through the dielectric at a fixed voltage, but will disappear at a somewhat lower voltage (say 1kV).
The 10W resistor is physically large and intended to not break over if the capacitor shorts. If your supply is capable of a lot of current, more precautions may be necessary so this is just a preliminary though. Safety is paramount, so get this checked out by someone local and competent before flipping the power on.
You could build a simple battery powered circuit that was floated up to 10 kV and measured the current flowing into the capacitor. Clearly care needs to be taken to ensure that this "simple circuit" was well insulated.
How to extract the current value measured - the simple circuit could be a voltage controlled oscillator driving an LED and, at some safe distance, a photodiode could pick up the signal and this can be measured on a frequency counter thus you know the current taken by the capacitor.