We have recently performed experiments with polarized deuteron beams at the Radioactive Isotope Beam Factory (RIBF). Tensor- and vector-polarized deuterons were produced using the RIKEN polarized ion source (PIS) , which is an atomic-beam-type ion source equipped with an electron cyclotron resonance (ECR) ionizer, and were accelerated to 190 MeV/u, 250 MeV/u, and 300 MeV/u with a cyclotron cascade. To measure the various spin observables, the spin orientation of the deuteron beams was freely directed by using a Wien filter. The advantage of this method is that since the velocity of the deuteron is low the size of a magnet required for the spin rotation is very compact. On the other hand it is crucial to realize strict single-turn extraction for each cyclotron because the cyclotron magnetic field causes precession of the deuteron spin resulting in a deviation between its spin orientation and the beam propagation direction. This paper describes the acceleration of the polarized deuteron beams by the RIBF accelerators and the method to confirm single-turn extraction.