In view of the wide applications of plasmonic vortices, a uniform theory of plasmonic vortex generation is advanced based on a metasurface consisting of nanometric rectangular holes. Rectangular holes may be located on one circle, two concentric circles, one spiral or two parallel spirals. The key problem in generating the plasmonic vortex is to construct a spiral phase, which can be excited by single or double holes. Theoretical analysis for generation of the plasmonic vortex is implemented in terms of the radiation model of dipoles and the propagation rule of surface plasmon polaritons. Several practical examples are presented and theoretical predictions are verified by the generated plasmonic vortices. The proposed theory is of benefit to the design of plasmonic vortex generators and the applications of plasmonic vortices.