Can an ordinary multimeter measure voltage in the uA level. If not, how can I measure it accurately?

Thanks.

 

Voltage is measured in volts, mV and uV. Current is measured in Amps, mA and uA.
A cheap multimeter can measure Amps. A good multimeter can measure mA. My Fluke measures down to 1mA. It can measure volts down to 0.1mVDC or 1.0mVAC.

 

You may need a microammeter for those measurements.