Capacitive current is short for capacitve charging current or better charging current of a capacitor. A capacitor is an electronics component that stores charge depending on the potential applied to it.
The charged surface of an electrode and the ions in the solution attract each other and form two separated layers of charge at the electrode solution interface. These two layers act as a capacitor. So there are now two ways how current can flow through the cell. The capacitive charging current and the Faraday current.
A more detailed view is available in the knowledge base article about capacitive current.
The Cottrell Experiment and Diffusion Limitation 3/3 – Electrochemical Double Layer
In this chapter the electrochemical double layer and its features are discussed. The electrochemical double layer acts as a capacitor and every change in the potential of the electrode will induce a capacitive charging current that is caused by physics not by a chemical reaction. This current decays exponentially.
If the potential of the electrode is changed, for example during a potential step, the amount of charge the capacitor stores changes, and a current will flow that has no chemical but only a physical meaning. This is the current that charges or discharges the capacitor also known as capacitive charging current or short capacitive current.