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Using a large sample of galaxies from the seventh data release of the Sloan Digital Sky Survey (SDSS-DR7), we have analyzed the alignment of disk galaxies around cosmic voids. We have constructed a complete sample of cosmic voids (devoid of galaxies brighter than Mr - 5 log h = -20.17) with radii larger than 10 h-1 Mpc up to redshift 0.12. Disk galaxies in shells around these voids have been used to look for particular alignments between the angular momentum of the galaxies and the radial direction of the voids. We find that disk galaxies around voids larger than ≳ 15 h-1 Mpc within distances not much larger than 5 h-1 Mpc from the surface of the voids present a significant tendency to have their angular momenta aligned with the void's radial direction with a significance ≳ 98.8% against the null hypothesis. The strength of this alignment is dependent on the void's radius and for voids with a radius ≲ 15 h-1 Mpc the distribution of the orientation of the galaxies is compatible with a random distribution. Finally, we find that this trend observed in the alignment of galaxies is similar to the one observed for the minor axis of dark matter halos around cosmic voids found in cosmological simulations, suggesting a possible link in the evolution of both components. [ABSTRACT FROM AUTHOR]