A metasurface is a planar optical device that controls the phase, amplitude, and polarization of light through subwavelength-scale unit elements, called meta-atom. The tunability of plasmonic vortex lens (PVL) which generates surface plasmon polaritons (SPPs) carrying orbital angular momentum can be improved by using meta-atom. However, conventional PVLs exhibit nonuniform field profiles according to the incident polarization states owing to the spin-orbital interaction (SOI) effect observed during SPP excitation. This paper describes a method of compensating for SOI of PVL by using the geometric phase of distributed nanoslits in a gold film. By designing the orientation angles of slit pairs, the anti-phase of the SOI effect can be generated for compensatory effect. In addition, polarization-independent PVLs are designed by applying a detour phase based on the position of the slit pairs. PVLs for center-, off-center-, and multiple-focus cases are demonstrated and measured via a near-field scanning microscope.