  Zeta Ori A is a hot star claimed to host a weak magnetic field, but no clear
magnetic detection was obtained so far. In addition, it was recently shown to
be a binary system composed of a O9.5I supergiant and a B1IV star. We aim at
verifying the presence of a magnetic field in zeta Ori A, identifying to which
of the two binary components it belongs (or whether both stars are magnetic),
and characterizing the field.Very high signal-to-noise spectropolarimetric data
were obtained with Narval at the Bernard Lyot Telescope (TBL) in France.
Archival HEROS, FEROS and UVES spectroscopic data were also used. The data were
first disentangled to separate the two components. We then analyzed them with
the Least-Squares Deconvolution (LSD) technique to extract the magnetic
information. We confirm that zeta Ori A is magnetic. We find that the
supergiant component zeta Ori Aa is the magnetic component: Zeeman signatures
are observed and rotational modulation of the longitudinal magnetic field is
clearly detected with a period of 6.829 d. This is the only magnetic O
supergiant known as of today. With an oblique dipole field model of the Stokes
V profiles, we show that the polar field strength is ~ 140 G. Because the
magnetic field is weak and the stellar wind is strong, zeta Ori Aa does not
host a centrifugally supported magnetosphere. It may host a dynamical
magnetosphere. Its companion zeta Ori Ab does not show any magnetic signature,
with an upper limit on the undetected field of $\sim$ 300 G.
