Many planet candidates have been detected by radial-velocity variations of the primary star; they are planet candidates, because of the unknown orbit inclination. Detection of the wobble in the two other dimensions, to be measured by astrometry, would yield the inclination and, hence, true mass of the companions. We aim to show that planets can be confirmed or discovered in a close visual stellar binary system by measuring the astrometric wobble of the exoplanet host star as a periodic variation of the separation, even from the ground. We test the feasibility with HD 19994, a visual binary with one radial velocity planet candidate. We use the adaptive optics camera NACO at the VLT with its smallest pixel scale (∼ 13 mas) for high-precision astrometric measurements. The separations measured in 120 single images taken within one night are shown to follow white noise, so that the standard deviation can be divided by the square root of the number of images to obtain the precision. In this paper we present the first results and investigate the achievable precision in relative astrometry with adaptive optics. With careful data reduction it is possible to achieve a relative astrometric precision as low as 50 μ as for a 0″.6 binary with VLT/NACO observations in one hour, the best relative astrometric precision ever achieved with a single telescope from the ground. The relative astrometric precision demonstrated here with AO at an 8-m mirror is sufficient to detect the astrometric signal of the planet HD 19994 Ab as periodic variation of the separation between HD 19994 A and B.