The entropy S of the horizon \theta = \pi /2 of the Hawking wormhole written in spherical Rindler coordinates is computed in this paper. Using Padmanabhan's prescription, we found that the surface gravity of the horizon is constant and equals the proper acceleration of the Rindler observer. S is a monotonic function of the radial coordinate \xi and vanishes when \xi equals the Planck length. In addition, its expression is similar with the Kaul--Majumdar one for the black hole entropy, including logarithmic corrections in quantum gravity scenarios.

PACS numbers: 04.60.--m, 02.40.--k, 04.90.+e