In this paper, we adapt the robust reversible watermarking modulation originally proposed by Vleeschouwer for images to the protection of relational databases. The resulting scheme modulates the relative angular position of the circular histogram center of mass of one numerical attribute for message embedding. It can be used for verifying database authentication as well as for traceability when identifying database origin after it has been modified. Beyond the application framework, we theoretically evaluate the performance of our scheme in terms of capacity, distortion, and robustness against two common database modifications: 1) addition and 2) removal of tuples. To that end, we model the impact of the embedding process and of database modifications on the probability distribution of the center of mass position. We further verify experimentally these theoretical limits within the framework of a medical database of more than one million of inpatient hospital stay records. We show that under the assumptions imposed by the central limit theorem, experimental results fit the theory. We also compare our approach with two recent and efficient schemes so as to prove its benefits.