Star's wobble due to orbiting planet
The presence of a planet orbiting a star is reflected in the star's motion. In fact, both the star and the planet orbit the common centre of mass. Since most of the mass in the star-planet system is concentrated in the star, the centre of mass is located within the star (marked with a cross).
The motion of the star, wobbling around the centre of mass, can be detected either via astrometry, by measuring how the star's position varies over time, or via the radial velocity technique, by measuring periodic shifts of absorption lines in the spectrum of the star.