Elliptical galaxies contain X-ray emitting gas that is subject to continuous ram pressure stripping over timescales comparable to cluster ages. The gas in these galaxies is not in perfect hydrostatic equilibrium. Supernova feedback, stellar winds, or active galactic nuclei (AGN) feedback can significantly perturb the interstellar medium (ISM). Using hydrodynamical simulations, we investigate the effect of subsonic turbulence in the hot ISM on the ram pressure stripping process in early-type galaxies. We find that galaxies with more turbulent ISM produce longer, wider, and more smoothly distributed tails of the stripped ISM than those characterised by weaker ISM turbulence. Our main conclusion is that even very weak internal turbulence, at the level of <15% of the average ISM sound speed, can significantly accelerate the gas removal from galaxies via ram pressure stripping. The magnitude of this effect increases sharply with the strength of turbulence. As most of the gas stripping takes place near the boundary between the ISM and the intraclustermedium (ICM), the boost in the ISM stripping rate is due to the random walk of the ISM from the central regions of the galactic potential well to larger distances, where the ram pressure is able to permanently remove the gas from galaxies. The ICM can be temporarily trapped inside the galactic potential well due to the mixing of the turbulent ISM with the ICM. The galaxies with more turbulent ISM, yet still characterised by very weak turbulence, can hold larger amounts of the ICM. [Abridged]