We show that charge transfer through a small superconducting (S) island of a single-electron transistor is strongly affected by vorticity. This interplay of charge and rotational degrees of freedom in a mesoscopic superconductor occurs through the effect of vorticity on the quantum mechanical spectrum of electron-hole excitations. The subgap quasiparticle levels in vortices can host an extra electron, thus suppressing the so-called parity effect in the S island. We propose to measure the collective dynamics of vorticity and electric charge via the charge pumping effect caused by alternating vortex entry and exit controlled by a periodic magnetic field.