The datasheet shows typical input bias current of 40na and max of 100na, depending on which ones you see.
That's almost 10% of 1ua.
On the other hand, most (genuine) opamps will come within the spec so maybe you will get luck so give it a try - if it doesn't pass, you can try other alternatives:
1) alternative #1: use a jfet. Go to your local radioshack and get a TL0xx: they have a typical input bias current of less than 1na (10-20pa typically).
2) alternative #2: put a mosfet pair in front of your opamp - this is often used to improve input stage performance or to add output offset adjustment capabilities.
Here is a basic nanoammeter, with a nmos input buffer, with a 1v/1ua gain, set by R4.
For it to be practical, you will need to implement offset adjustment (easily done on the input's legs), etc. Resistor values, aside from R4, are not critical.