Balmer lines emitted from a Penning discharge in hydrogen gas show a Doppler shift indicating rotation around the axis of the discharge column. This effect is explained as a result of the charge exchange collisions of the drifting plasma ions with the neutral atoms, and the fast neutral particle thus produced being excited by the plasma electrons. Accordingly we identify this rotation with the drift motion of the plasma. The velocity of rotation vrot is obtained as a function of radius from the measured Doppler shifts for two values of the confining magnetic field strength Bz The results show that for plasma layers with radial distances r smaller than or equal to the radius of the hollow anode cylinder, that means inside a tube which contains radial currents Ir, the rotational speed vrot can be expressed by the following very simple formula: vrot = (IrBz / nimin0 σcoll2πrL)1/2. A derivation of this expression is given.