We introduce a machine-learning interatomic potential for tungsten using the Gaussian Approximation Potential framework. We specifically focus on properties relevant for simulations of radiationinduced collision cascades and the damage they produce, including a realistic repulsive potential for the short-range many-body cascade dynamics and a good description of the liquid phase. Furthermore, the potential accurately reproduces surface properties and the energetics of vacancy and self-interstitial clusters, which have been long-standing deficiencies of existing potentials. The potential enables molecular dynamics simulations of radiation damage in tungsten with unprecedented accuracy.