Context: The historic plates of the Carte du Ciel, an international cooperative project launched in 1887, offers valuable first-epoch material for determining of absolute proper motions. Aims: We present an original method of digitizing and astrometrically reducing Carte du Ciel plate material using an inexpensive flatbed scanner, to demonstrate that for this material there is an alternative to more specialized measuring machines that are very few in number and thus not readily available. The sample of plates chosen to develop this method are original Carte du Ciel plates of the San Fernando zone, photographic material with a mean epoch 1903.6, and a limiting photographic magnitude ~14.5, covering the declination range of -10° ≤ δ ≤ -2°. Methods: Digitization has been made using a commercial flatbed scanner, demonstrating the internal precision that can be attained with such a device. A variety of post-scan corrections are shown to be necessary. In particular, the large distortion introduced by the non-uniform action of the scanner is modelled using multiple scans of each plate. We also tackle the specific problems associated with the triple-exposure images on some plates and the réseau grid lines present on all. The final measures are reduced to celestial coordinates using the Tycho-2 Catalogue. Results: The internal precision obtained over a single plate, 3~μ m ˜ 0.18 arcsec in each axis, is comparable to what is realized with similar plate material using slower, less affordable, and less widely available conventional measuring machines, such as a PDS microdensitometer. The accuracy attained over large multi-plate areas, employing an overlapping plate technique, is estimated at 0.2 arcsec. Conclusions: The techniques presented here for digitizing photographic material provide a fast and readily available option for the exploitation of old plate collections. Our demonstration area, consisting of ~560 000 stars at an average epoch of 1901.4, is presented as a practical example of the developed scanning and reduction methods. These results are currently being combined with modern astrometry to produce an absolute proper-motion catalogue whose construction is underway.