Easy:

Use a pair of diodes.
One charges the cap through a known 1% resistor.
The other discharges the cap through the unknown.

The cap value is common to both measurements, and cancels out.

You need a schmidt input for this, something with high and low thresholds
that are not both at VCC/2. An HC14 works well.

You are measuring the time it takes to charge/discharge C from VthLow, to
VthHigh and back down again.

Measurement is a little complicated, but not bad.
Start with the cap charged (reading a "1")
Discharge till you get a zero, then IMMEDIATELY change the output to charge
again, and measure the time taken to get there.
When you get there, IMMEDIATELY set to discharge, and measure the time it
takes to get to "0" again.
You can average up the measurements.

If you don't immediately reverse on hitting the threshold, then you risk
charging to some unknown voltage, (not the threshold)

If this isn't practical, then arrainge the HC14 as an RC oscillator through
the diodes and resistors, and simply measure the high and low times.

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