I'm working with the attached design and I'm trying to figure out the input impedance. I've always heard that op amp have a very high input impedance but this circuit seems to have one that's quite low (as it loads down the driving source)

 

Rin=47K

 

The input impedance of the op-amp will be high, but that of your circuit will be 47k. As you have negative feedback, the inverting input will behave as a virtual ground - near zero impedance. That leaves just the resistance of the input resistor.

A non-inverting buffer will maintain the high impedance of the amplifier input.

 

The TL series op-amps have an input impedance of 10 to the 12th power.
The op-amp is not the problem. It's the circuit configuration that is determining the input impedance.
You could easily scale the resistors to a much higher impedance if you could find a potentiometer that will fit.
You can buy trimmers up to 500 megs.
http://www.mouser.com/Passive-Components/Potentiometers-Trimmers-Rheostats/_/N-9q0yi?P=1z0vkoa
The consideration there is how much noise you will pick up if the circuit has an input impedance of 4.7 meg.

Something has to change if you are to avoid loading down the input signal, but there are several choices in how to do that.