Soliton rain is a bunch of small soliton pulses slowly drifting near the main pulse having the period of a round trip. For Er-doped fiber laser mode-locked by carbon nanotubes, for the first time, we demonstrate both experimentally and theoretically a new type of polarization attractors controllable by vector soliton rain. With adjusting the pump power, vector soliton rain takes the form of pulses with rotating states of polarization which enable transforming slowly evolving trajectories on the Poincaré sphere from the double-scroll spiral to the circle. The obtained results on controlling complex multisoliton dynamics can be of interest in laser physics and engineering with potential applications in spectroscopy, metrology, and biomedical diagnostics.