Sure. You just need design and make a PEM where the membrane conductivity is the limiting factor. The catalyst layers and the membrane contribute to the overall resistance. By minimizing the contribution form the catalyst layers, the resistance of the membrane can be measured. This can be achieved either by very high loading and high flux of fuel gases or a very thick membrane. Now, by doing a normal CV, you should be able to extract the resistivity( conductivity) of the membrane.  

Another option to have proton conductivity may be obtained using electrochemical impedance spectroscopy. 

We routinely measure our membrane conductivity by 4-point probe using EIS (measured in RH-chamber outside the fuel cell)

personally speaking, CV is not so convincible to determine the conductivity or resistance property. EIS is a good one.

EIS is preferably because it allows us to separate the charge transfer at the interface and charge transport phenomena within the phases. I’d recommend you to perform an experiment for determination of temperature influence on conductivity. These data are well characterize your materials and the conductivity types.

I agree with Roto and Dennis, do EIS measurements , but remember to display the results as log Z1(w) and log Z2(w) versus log(w) (and possibly the same for complex capacitance representation). One of the flat parts in Z1(w) is your PEM proton resistance

Petr