You could used a  some rheometer or a dielectric equimment as for example of TA instrument.

Provided that the density of the fiber is known (thus the volume fraction can be calculated) and if the fibers can be reasonably aligned, you can measure the dielectric properties of parallel fiber bundles (in sheet or in coaxial form) and calculate back the bulk properties using dielectric mixture formulae.

Thank all of you for answers. A will find dielectric mixture formula.

Pls find attached a review article on such formulate. You can get the relevant formulae using and l/d in the infinite limit. If you make the measurement perpendicularly to the fiber direction, you should take the proper depolarizattion factor.

Thank you very much for the paper

The best way to get the dielectric permittivity of a single fiber (not of a bundle) caused by the electronic and ionic polarization is to measure it microwaves using the method for the needle-shaped speciments described in the book by J. Grigas "Microwave Dielectric Spectroscopy of Ferroelectrics and Relater Materials (Gordon & Breach Publ., USA).

It will give multi information. I hope you are interested in measuring dielectric permittivity (not only dielectric constant i.e. static value of the permittivity). Of course you will get the level of permeation of the electric field. Beside you may get (energy) loss through the medium (either parallel or perpendicular to fibers). If you are interested you may get refractive indices by measuring permittivity at very high frequencies. Of course you will have to design proper sample cell to be used with measuring instruments i.e. impedance analyzers of various manufacturers e.g. Solartron, Nova Control, Agilent etc.