Quantum particles can penetrate potential barriers by tunnelling. If that barrier is rotating, the tunnelling process is modified. This is typical for electrons in atoms, molecules or solids exposed to strong circularly polarized laser pulses. Here we measure how the transmission probability through a rotating tunnel depends on the sign of the magnetic quantum number m of the electron and thus on the initial direction of rotation of its quantum phase. We further show that our findings agree with a semiclassical picture, in which the electron keeps part of that rotary motion on its way through the tunnel by measuring m-dependent modification of the electron emission pattern. These findings are relevant for attosecond metrology as well as for interpretation of strong-field electron emission from atoms and molecules and directly demonstrate the creation of ring currents in bound states of ions with attosecond precision. In solids, this could open a way to inducing and controlling ring-current-related topological phenomena.