ω Ori is a B2IIIe star for which rotational modulation and non-radial pulsations (NRP) have been recently investigated from two independent observational campaigns in 1998 and 1999. Putting the data of these 2 campaigns together, and adding data obtained in 2001, we search for multiperiodicity in the line profile variations and evidence for outbursts. From new spectropolarimetric data obtained at the Télescope Bernard Lyot (TBL, Pic du Midi, France) in 2001 we also measure the Stokes V parameter in the polarised light. We find evidence for the presence of a weak magnetic field in ω Ori sinusoidally varying with a period of 1.29 d. The equivalent widths (EW) of the wind sensitive UV resonance lines also show a variation with the same period, which we identify as the rotational period of the star. We propose an oblique rotator model and derive G to explain the observations. Moreover, we carry out an abundance analysis and find the star to be N-enriched, a property which is shared with other magnetic stars. We propose ω Ori as the first known classical Be star hosting a magnetic field.