In principle, the resistivity of bulk FCC cubic materials should not depend on the orientation due to the fact that the conductivity tensor is single valued. However, we show that this conclusion is not valid for thin films. Deposition of highly oriented Al, Ag, and Cu films on amorphous substrates using the partially ionized beam (PIB) technique exhibit a resistivity which is strongly correlated with the texture, i.e., the tighter the texture, the lower the film resistivity. We model the film as an array of grains whose grain boundaries can be considered as delta function potentials for electron scattering and the strength of the potentials can be calculated from the measured resistivity of the films. On the other hand, the fiber texture distribution of the the films is obtained from X-ray pole figure measurements, and Monte-Carlo simulations are then performed using this data to determine the average dislocation density at the grain boundaries due to the grain to grain crystallographic mismatch. We show that the transmittance coefficient for electron scattering, and therefore the film resistivity, is a monotonically increasing function of the average dislocation density. We therefore conclude that the structure of grain boundaries in a thin film provides the necessary mechanism by which the resistivity of an FCC cubic metal can depend on the texture.