The Faraday rotation measures of 38 extragalactic sources have been measured with the Very Large Array in order to provide new information on the properties of plasma turbulence in the interstellar medium. Of particular interest is the possibility that such Faraday rotation measurements can provide information on the magnetic field component of interstellar turbulence. The observations were made in an area of the sky from 1(h)50(m) to 3(h)10(m) right ascension and from 32 degrees to 44 degrees declination. This area is unique in that it is the only region away from the Galactic plane where the Ha intensity has been mapped completely, both spatially and in velocity. The rotation measures were found to vary in a relatively smooth fashion across the entire region. The magnitudes of the mean rotation measure and emission measure were found to be consistent with a simple Galactic model consisting of an exponential disk of scale height 1 kpc and midplane density 0.03 cm(-3), together with an azimuthal or bisymmetric spiral Galactic magnetic field of 3-4 mu G. The structure functions of rotation measure and emission measure were analyzed in order to extract information on the nature of the plasma turbulence in the interstellar medium in this direction. A comparison was made between the observed rotation and emission measure structure functions and theoretical structure function expressions, which are presented here for the first time. We find that the observed structure functions are consistent with a turbulence model in which both density and magnetic field fluctuations have Kolmogorov spectra. The outer scale of this turbulence is about 4 pc. For larger scales (corresponding to angular spacings delta theta greater than or equal to 0 degrees.1) the turbulence appears to be two-dimensional. For all angular scales, the level of the rotation measure structure function is larger than would be expected from only plasma density fluctuations of known characteristics in an otherwise uniform Galactic magnetic field. The data require, in addition to the plasma density fluctuations, a turbulent magnetic field with a rms amplitude of similar to 1 mu G. To the authors' knowledge, this represents the first measurement of magnetic field fluctuations in the interstellar plasma on spatial scales that appropriately may be described as turbulence.
