It looks like you might be able to do:
REG_PIOx_ODSR = data_to_set;
to set output data, and:
input_data = REG_PIOx_PDSR;
to get input data, where x is A,B,C or D. The acronyms are "output data status register" and "pin data status register". You may first need to enable output by writing ones to PIOx_OWER (output write enable register). If you've already used standard arduino calls to set the pin in question to be an output, I think that's all you'll need to do. See page 646 of the datasheet for more info:
The registers all follow the same naming convention, it's always REG_PIOx_, so it's easy to translate register names in the datasheet to variable names in your sketch.
I can't test as I don't have a Due yet, I'd love to know if this works though.