The traditional op-amp is a voltage type. Meaning: the output is constant voltage, and the input-to-output characteristic is very high voltage gain and very low input current (at DC, that is).
A current type amp wouldn't be terribly hard to make or use, but I don't think it exists as a product. There are "current mode op-amps", but these are current input only; they still deliver output voltage (so exhibit very high transconductance, instead of dimensionless voltage or current gain). So you're kind of left making a half-assed one out of transistors and op-amps.
Tim