No, just measure the change in voltage before and after injecting charge - capacitors integrate charge. It does require leakage currents to be small enough not to matter on the timescale of the two measurements though. But its easier to adjust a pulse width to fractions of a microsecond than take analog measurements a fraction of a microsecond apart.
I think the point of this question is to determine what resistor value is needed for a given cable and risetime requirement, ie measure the capacitance.
Personally I'd just calculate the capacitance from the datasheet for the cable, its length, and the input capacitances of the loads, then multiply by a suitable safety factor. Twisted pair is around 50pF/m, most coax is around 80pF/m.
But note that fast logic busses like I2C and SPI are not designed to travel far, so really there shouldn't be much cable anyway. Long cables bring problems like ringing and reflections so you need to worry about those too.