No, you also need some way to measure the velocity of the particles in a liquid (electrophoresis) or the velocity of liquid past a surface (electroosmosis).
The zeta potential is the voltage at the shear plane around the Debye layer, where solvent molecules are free to move. So unless there is electrophoretic movement, it cannot be accessed experimentally. That said, the open circuit potential setting on a typical commercial pstat could be used to measure a voltage, basically using the ocp input as an electrometer.