When a cylinder is mounted on an elastic support within a current, vortex-induced vibrations (VIV) may occur down to a Reynolds number ( Re ) close to $20$ , based on the body diameter ( $D$ ) and inflow velocity ( $U$ ), i.e. below the critical value of $47$ reported for the onset of flow unsteadiness when the body is fixed. The impact of a forced rotation of the elastically mounted cylinder on the system behaviour is explored numerically for $Re \leqslant 30$ , over wide ranges of values of the rotation rate (ratio between body surface velocity and $U$ , $\alpha \in [0,5]$ ) and reduced velocity (inverse of the oscillator natural frequency non-dimensionalized by $D$ and $U$ , $U^\star \in [2,30]$ ). The influence of the rotation is not monotonic, but the most prominent effect uncovered in this work is a substantial enhancement of the subcritical- Re , flow-induced vibrations beyond $\alpha =2$ . This enhancement is twofold. First, the rotation results in a considerable expansion of the vibration/flow unsteadiness region in the $({Re},U^\star )$ domain, down to $Re=4$ . Second, the elliptical orbits described by the rotating body are subjected to a major amplification, with a transition from VIV to responses whose magnitude tends to increase unboundedly with $U^\star$ , even though still synchronized with flow unsteadiness. The emergence of such galloping-like oscillations close to the onset of vibrations disrupts the scenario of gradual vibration growth with Re , as amplitudes larger than $10$ body diameters may be observed at $Re=10$ .