(abridged) In the frame of the search for extrasolar planets and brown dwarfs
around early-type main-sequence stars, we present the results obtained on the
early F-type star Theta Cygni. Elodie and Sophie at OHP were used to obtain the
spectra. Our dedicated radial-velocity measurement method was used to monitor
the star's radial velocities over five years. We also use complementary, high
angular resolution and high-contrast images taken with PUEO at CFHT. We show
that Theta Cygni radial velocities are quasi-periodically variable, with a
~150-day period. These variations are not due to the ~0.35-Msun stellar
companion that we detected in imaging at more than 46 AU from the star. The
absence of correlation between the bisector velocity span variations and the
radial velocity variations for this 7 km/s vsini star, as well as other
criteria indicate that the observed radial velocity variations are not due to
stellar spots. The observed amplitude of the bisector velocity span variations
also seems to rule out stellar pulsations. However, we observe a peak in the
bisector velocity span periodogram at the same period as the one found in the
radial velocity periodogram, which indicates a probable link between these
radial velocity variations and the low amplitude lineshape variations which are
of stellar origin. Long-period variations are not expected from this type of
star to our knowledge. If a stellar origin (hence of new type) was to be
confirmed for these long-period radial velocity variations, this would have
several consequences on the search for planets around main-sequence stars, both
in terms of observational strategy and data analysis. An alternative
explanation for these variable radial velocities is the presence of at least
one planet of a few Jupiter masses orbiting at less than 1 AU. (abridged)Comment: 9 pages, accepted in A