The neural interface system of one embodiment includes a cylindrical shaft, a lateral extension longitudinally coupled to at least a portion of the shaft and having a thickness less than a diameter of the shaft, and an electrode array arranged on the lateral extension and radially offset from the shaft, including electrode sites that electrically interface with their surroundings. The method of one embodiment for making the neural interface system includes forming a planar polymer substrate with at least one metallization layer, patterning on at least one metallization layer an electrode array on a first end of the substrate, patterning conductive traces on at least one metallization layer, rolling a portion of the substrate toward the first end of the substrate, and securing the rolled substrate into a shaft having the first end of the substrate laterally extending from the shaft and the electrode array radially offset from the shaft.