Context. For the past thirty years, modern ground-based time-series of the solar radius have shown different apparent variations according to different instruments. The origins of these variations may result from the observer, the instrument, the atmosphere, or the Sun. Solar radius measurements have been made for a very long time and in different ways. Yet we see inconsistencies in the measurements. Numerous studies of solar radius variation appear in the literature, but with conflicting results. These measurement differences are certainly related to instrumental effects or atmospheric effects. Use of different methods (determination of the solar radius), instruments, and effects of Earth's atmosphere could explain the lack of consistency on the past measurements. A survey of the solar radius has been initiated in 1975 by Francis Laclare, at the Calern site of the Observatoire de la Côte d'Azur (OCA). Several efforts are currently made from space missions to obtain accurate solar astrometric measurements, for example, to probe the long-term variations of solar radius, their link with solar irradiance variations, and their influence on the Earth climate. Aims. The Picard program includes a ground-based observatory consisting of different instruments based at the Calern site (OCA, France). This set of instruments has been named "Picard Sol" and consists of a Ritchey-Chrétien telescope providing full-disk images of the Sun in five narrow-wavelength bandpasses (centered on 393.37, 535.7, 607.1, 782.2, and 1025.0 nm), a Sun-photometer that measures the properties of atmospheric aerosol, a pyranometer for estimating a global sky-quality index, a wide-field camera that detects the location of clouds, and a generalized daytime seeing monitor allowing us to measure the spatio-temporal parameters of the local turbulence. Picard Sol is meant to perpetuate valuable historical series of the solar radius and to initiate new time-series, in particular during solar cycle 24. Methods. We defined the solar radius by the inflection-point position of the solar-limb profiles taken at different angular positions of the image. Our results were corrected for the effects of refraction and turbulence by numerical methods. Results. From a dataset of more than 20,000 observations carried out between 2011 and 2013, we find a solar radius of 959.78 ±0.19 arc-seconds (696,113 ±138 km) at 535.7 nm after making all necessary corrections. For the other wavelengths in the solar continuum, we derive very similar results. The solar radius observed with the Solar Diameter Imager and Surface Mapper II during the period 2011-2013 shows variations shorter than 50 milli-arc-second that are out of phase with solar activity.