The climate of a terrestrial exoplanet is controlled by the type of host star, the orbital configuration, and the characteristics of the atmosphere and the surface. Many rocky exoplanets have higher eccentricities than those in the Solar system, and about 18 per cent of planets with masses <10 M-circle plus have e > 0.1. Underexplored are the implications of such high eccentricities on the atmosphere, climate, and potential habitability on such planets. We use WACCM6, a state-of-the-art fully coupled Earth-system model, to simulate the climates of two Earth-like planets: one in a circular orbit (e = 0), and one in an eccentric orbit (e = 0.4) with the same mean insolation. We quantify the effects of eccentricity on the atmospheric water abundance and loss given the importance of liquid water for habitability. The asymmetric temperature response in the eccentric orbit results in a water vapour mixing ratio in the stratosphere ( >20 ppmv) that is approximately five times greater than that for circular orbit (similar to 4 ppmv). This leads to at most similar to 3 times increases in both the atmospheric hydrogen loss rate and the ocean loss rate compared with the circular case. Using the Planetary Spectrum Generator, we simulate the idealized transmission spectra for both cases. We find that the water absorption features are stronger at all wavelengths for the e = 0.4 spectrum than for the circular case. Hence, highly eccentric Earth-like exoplanets may be prime targets for future transmission spectroscopy observations to confirm, or otherwise, the presence of atmospheric water vapour.