You could use a transimpedance amplifier, which will also have to run on batteries (you possibly could be clever with a PSU).
This is only of use if the current draw by your uC is low and can be supplied through the amplifier's feedback impedance. The op amps bias current and offset voltage will be a source of error. These can be ignored depending on your required accuracy or nulled out.
See
https://en.wikipedia.org/wiki/Transimpedance_amplifierI have used this technique to measure currents from 10s of milliamps to around 5pA (I used logarithmic feedback to get that dynamic range) and have used a simple resistor 1Meg ohm resistor around a CMOS amplifier powered from a 9V battery to measure a few microamps full scale. Fractions of a microamp resolution should not present too much of a problem.
The connection is unusual, ask if you need help - I can't add a diagram from here (at work).
Let us know how you get on

Stephen