Here is a feature of capacitors which could conceivably have caused you to believe, against the advice of your (unreferenced) text book, that an uncharged capacitor with only one leg connected to a current source could be given a charge albeit as you admit a small one.
This answer takes a small number of steps and begins at wikipedia: https://en.wikipedia.org/wiki/Electrostatic_induction
At Wikipedia, scroll to the heading Induction in dielectric objects. It doesn't necessarily mean dielectrics in a capacitor, but in this case the nomenclature is exact.
To precis Wikipedia simply, a charge across the dielectric will distort the positioning of electron orbits around the nuclii of the atoms in the dielectric. When the charge of the conductors on each side of the dielectric is removed, the electron orbits in the dielectric atoms returns to normal. But not immediately.
My government's NZ Post Office Radio Training School (Wellington NZ, lecturer Grant,I. 1964), introduced this atomic distortion in capacitors which slowly return to normal when a DC charge was removed, by the term dielectric hysteresis (from my lecture notes). We students were told to short circuit capacitor terminals on any capacitor taken out of service which had been carrying high DC voltages, and leave the short circuit in place until the capacitor was re-installed.
Now to you. Did you by any chance build a practical circuit as described to experiment on before you asked your question, or are you being hypothetical as to the possibility of a "one-lead" capability to charge a capacitor because of some seemingly anomalous feature you may have observed in a DUT, particularly a high voltage circuit and under specific test conditions?
Here is my accidentally derived empirical data so you know where I am coming from: I removed a 4uF oiled paper capacitor which had been working at 5,000VDC from a valve transmitter. Left the terminals shortcircuited for 2-3 weeks. Removed the short for a subsequent 2 weeks. Thought I should replace the short before physically moving a very large and very heavy capacitor elsewhere, and with a flash and a bang the capacitor demonstrated that dielectric hysteresis rebuilt an estimated 5-10 percent of charge after weeks of short circuit.
A genuine, significant charge on a capacitor that had had "nothing" hooked up to its terminals for weeks.
Hopefully this answer may explain a possibility how you may have developed your hypothesis which negates the text book?