The exclusive electroproduction of rho-0 mesons was studied with the HERMES spectrometer at the DESY laboratory by scattering 27.6 GeV positron and electron beams off a transversely polarized hydrogen target. Spin density matrix elements for this process were determined from the measured production- and decay-angle distributions of the produced rho-0 mesons. These matrix elements embody information on helicity transfer and the validity of s-channel helicity conservation in the case of a transversely polarized target. From the spin density matrix elements, the leading-twist term in the single-spin asymmetry was calculated separately for longitudinally and transversely polarized rho-0 mesons. Neglecting s-channel helicity changing matrix elements, results for the former can be compared to calculations based on generalized parton distributions, which are sensitive to the contribution of the total angular momentum of the quarks to the proton spin.