Well, this is only part of the story. What you want is a "current to voltage converter" circuit, which is basically an op amp with a resistor between the output and the inverting input. (The non-inverting input would be tied to a constant mid-value voltage that is proper for the scale's circuitry.) The sine wave current is also applied to the inverting input. The resistor value is chosen to get the uA current up to a meaningful (voltage) level. You can then "slice" this with a comparator or even a Schmitt trigger chip.
This will only give you the native resolution of the scale. So, if it has 100 lines/mm (10 um resolution) you will get 4X that in quadrature, so 400 counts/mm. If that is satisfactory, then it is easy. If that is NOT enough resolution, then you need an interpolator box, which will be somewhat expensive.
Jon
