Is there a way to plot the current to charge a capacitor given that there is a max current in the circuit given by the power supply?
With a 800 Volts DC supply, and a 200 k&Omega; resistor in series with the capacitor, the maximum current the charging will draw is 4 mA. 

How to calculate this:


Assume an ideal capacitor i.e. Zero Equivalent Series Resistance. Real capacitors and their leads can only increase this ESR.
At start of charging the current draw is maximum, as potential difference is maximum
At this time, I = V / R, V = 800 Volts and R = 200 k&Omega;
Thus Imax = 4 mA
As the capacitor charges up, this current will reduce further as per the normal RC curve.


As this is lower than the 20 mA supply limit, the supply-limited maximum current will not come into play at all.

EDIT: Note that the time constant of the resistor and capacitor is 47 seconds, which means that it will take that long to reach 63% of its final voltage. It will take 3&times; that long (2:21) to reach 95% and 5&times; that long (3:55) to reach 99%. You can reduce those numbers by a factor of 5 by reducing the resistor to 40K&Omega;, which would just touch the source limit of 20mA at the beginning of the charge cycle. If you simply charge the capacitor with a constant current of 20mA, it will take 9.4 seconds.