Structured light carrying orbital angular momentum (OAM) opens up a new physical dimension for studying light–matter interactions. Despite this, the complex fields created by OAM beams still remain largely unexplored in terms of their effects on surface plasmons. This paper presents a revelation of anomalous plasmon excitations in single particles and plasmon couplings of neighboring nanorods under OAM beams, which are forbidden using non-OAM sources. The plasmon excitation of single nanoparticles is determined both by photon spin angular momentum (SAM) and OAM and influenced by the locations of the nanoparticles. Specifically, when SAM and OAM are equal in magnitude and opposite in direction, a pure plasmon excitation along light propagation direction is achieved. Two plasmon dipoles show end-to-end antibonding coupling and side-by-side bounding coupling, which are the opposite of the typical couplings. Furthermore, we observe Fano resonance with a nanorod dimer: one aligned along light propagation direction acting as the bright mode and the other aligned along the global polarization direction of light acting as the dark mode, which is the opposite of the usual plasmonic Fano resonance. By taking advantage of the unique property of the OAM source, this investigation presents a novel way to control and study surface plasmons, and the research of plasmon behavior with OAM would open new avenues for controlling electromagnetic waves and enriching the spectroscopies with more degrees of freedom.