  Radial velocity (RV) measurements are used to search for planets orbiting
late-type main-sequence stars and confirm the transiting planets. The most
advanced spectrometers are approaching a precision of $\sim 10$ cm/s that
implies the need to identify and correct for all possible sources of RV
oscillations intrinsic to the star down to this level and possibly beyond. The
recent discovery of global-scale equatorial Rossby waves in the Sun, also
called r modes, prompted us to investigate their possible signature in stellar
RV measurements. R modes are toroidal modes of oscillation whose restoring
force is the Coriolis force and propagate in the retrograde direction in a
frame that corotates with the star. The solar r modes with azimuthal orders $3
\leq m \lesssim 15$ were identified unambiguously because of their dispersion
relation and their long e-folding lifetimes of hundreds of days. Here we
simulate the RV oscillations produced by sectoral r modes with $2 \leq m \leq
5$ assuming a stellar rotation period of 25.54 days and a maximum amplitude of
the surface velocity of each mode of 2 m/s. This amplitude is representative of
the solar measurements, except for the $m=2$ mode which has not yet been
observed. Sectoral r modes with azimuthal orders $m=2$ and $3$ would produce RV
oscillations with amplitudes of 76.4 and 19.6 cm/s and periods of 19.16 and
10.22 days, respectively, for a star with an inclination of the rotation axis
$i=60^{\circ}$. Therefore, they may produce rather sharp peaks in the Fourier
spectrum of the radial velocity time series that could lead to spurious
planetary detections. Sectoral r~modes may represent a source of confusion in
the case of slowly rotating inactive stars that are preferential targets for RV
planet search. The main limitation of the present investigation is the lack of
observational constraint on the amplitude of the $m=2$ mode on the Sun.
