A lattice model for active matter is studied numerically, showing that it displays wetting transitions between three distinctive phases when in contact with an impenetrable wall. The particles in the model move persistently, tumbling with a small rate α, and interact via exclusion volume only. When increasing the tumbling rates α, the system transits from total wetting to partial wetting and unwetting phases. In the first phase, a wetting film covers the wall, with increasing heights when α is reduced. The second phase is characterized by wetting droplets on the wall with a periodic spacing between them. Finally, the wall dries with few particles in contact with it. These phases present nonequilibrium transitions. The first transition, from partial to total wetting, is continuous and the fraction of dry sites vanishes continuously when decreasing the tumbling rate α. For the second transition, from partial wetting to dry, the mean droplet distance diverges logarithmically when approaching the critical tumbling rate, with saturation due to finite-size effects.