Objects of the Solar System can screen the cosmic rays as seen from the Earth. In particular, the cosmic shadows of the Moon and of the Sun have been observed in the last years by very large observatories. The latter can reveal details on the solar activity and magnetic field, an information which can be of high interest to better understand its internal dynamics. We report here on the possibility to perform such a study with much smaller and portable instruments. A compact muon telescope of active area 50 × 50cm2 was mounted on a motorized platform and followed the Sun during more than 7 months. By selecting muons close to the horizon, the data exhibit a small muon deficit in the direction of the Sun. These results suggest that a network of muon telescopes may be an interesting tool in the future for the continuous monitoring of the solar activity.