Depending on your application its not too hard to build a Zero resistance Ammeter with an OP amp/ It's also known as a Feedback Ammeter for low currents. for less than 10 mA it's pretty easy. 100 mA and tiny voltages it's much harder. I've done both. The general equation is Vout = Vb*-I*Rf. Vb is a bias voltage and note the sign change on the output. Ibias, Vos and unity gain stability are the most important OP-amp parameters. I don't have too much experience with single supply versions.
Without any heroic measures, I managed about 40 e-12 amps of offset current.