Localized surface plasmon resonance (LSPR) has been shown to exhibit a strong potential for nanoscale electromagnetic field manipulation beyond the diffraction limit. Particularly dark mode plasmons circumvent radiation loss and store the energy long in time, which raise the prospect of interesting plasmonics applications, for example biochemical sensing and nanoscale lasing. Here we theoretically investigate a method of exciting multipole plasmons, including dark modes, using normally incident light. By performing numerical calculations, we show that multipole plasmons in metal nanodisks can be selectively excited by circularly-polarized optical vortex beams. We study the electromagnetic fields of the beam cross-sections and their correspondence with the excited multipole plasmon modes with respect to spin and orbital angular momenta. The transfer of angular momentum between photons and plasmons is also discussed.