Context. R CrA is the brightest member of the Coronet star-forming region and is the closest Herbig AeBe star with a spectrum dominated by emission lines. Its luminosity has been monitored since the end of the nineteenth century, but the origin of its variability, which shows a stable period of 65.767 ± 0.007 days, is still unknown. Aims. We studied photometric and spectroscopic data for this star to investigate the nature of the variability of R CrA. Methods. We exploited the fact that the near-infrared luminosity of the Herbig AeBe stars is roughly proportional to the total luminosity of the stars to derive the absorption, and then mass and age of R CrA. In addition, we modeled the periodic modulation of the light curve as due to partial attenuation of a central binary by a circumbinary disk. This model reproduces the observations very well. Results. We found that the central object in R CrA is a very young (1.5 ± 1.5 Myr) highly absorbed (A_V = 5.47 ± 0.4 mag) binary; we obtain masses of M_A = 3.02 ± 0.43 M_⊙ and M_B = 2.32 ± 0.35 M_⊙ for the two components. We propose that the secular decrease of the apparent luminosity of R CrA is due to a progressive increase of the disk absorption. This might be related to precession of a slightly inclined disk caused by the recently discovered M-dwarf companion. This means that R CrA might be a triple system hosting a disk.