(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 stars 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)
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