Recently, two of us have found numerically rotating Ellis wormholes as solutions of 4-dimensional Einstein gravity coupled to a phantom field. In this paper, we investigate possible observational signatures to identify similar objects in the Universe. These symmetric wormholes have a mass and are compact, so they may look like black holes. We study the iron line profile in the X-ray reflection spectrum of a thin accretion disk around rotating Ellis wormholes and we find some specific observational signatures that can be used to distinguish these objects from Kerr black holes. We simulate some observations with XIS/Suzaku assuming typical parameters for a bright AGN and we conclude that current X-ray missions cannot apply strong constraints. ; Comment: 10 pages, 6 figures. v2: refereed version with simulated observations