Context. Carte du Ciel was a global international project at the end of the nineteenth and beginning of the twentieth century to map the sky to about magnitude 14 on photographic plates. The full project was never observationally completed and a large fraction of the observations made remain unanalyzed. Aims. We want to study whether the astrometric and photometric accuracies obtained for the Carte du Ciel plates digitized with a commercial digital camera are high enough for scientific exploitation of the plates. Methods. We use a digital camera Canon EOS 5Ds, with a 100 mm macrolens for digitizing. We analyze six single-exposure plates and four triple-exposure plates from the Helsinki zone of Carte du Ciel (+39^∘ ≤ δ ≤ +47^∘). Each plate is digitized using four images, with a significant central area being covered twice for quality control purposes. The astrometric calibration of the digitized images is done with the data from the Tycho-Gaia Astrometric Solution (Gaia TGAS) of the first Gaia data release (Gaia DR1), Tycho-2, Hot Stuff for One Year (HSOY), USNO CCD Astrograph Catalog (UCAC5), and PMA catalogs. Results. The best astrometric accuracy is obtained with the UCAC5 reference stars. The astrometric accuracy for single-exposure plates is σ(α cos(δ)) = 0.16″ and σ(δ)=0.15″, expressed as a Gaussian deviation of the astrometric residuals. For triple-exposure plates the astrometric accuracy is σ(α cos(δ)) = 0.12″ and σ(δ)=0.13″. The 1 − σ uncertainty of photometric calibration is about 0.28 mag and 0.24 mag for single- and triple-exposure plates, respectively. We detect the photographic adjacency (Kostinsky) effect in the triple-exposure plates. Conclusions. We show that accuracies at least of the level of scanning machines can be achieved with a digital camera, without any corrections for possible distortions caused by our instrumental setup. This method can be used to rapidly and inexpensively digitize and calibrate old photographic plates enabling their scientific exploitation.