Context. Transition disks are considered sites of ongoing planet formation, and their dust and gas distributions could be signposts of embedded planets. The transition disk around the T Tauri star RY Lup has an inner dust cavity and displays a strong silicate emission feature. Aims. Using high-resolution imaging we study the disk geometry, including non-axisymmetric features, and its surface dust grain, to gain a better understanding of the disk evolutionary process. Moreover, we search for companion candidates, possibly connected to the disk. Methods. We obtained high-contrast and high angular resolution data in the near-infrared with the VLT/SPHERE extreme adaptive optics instrument whose goal is to study the planet formation by detecting and characterizing these planets and their formation environments through direct imaging. We performed polarimetric imaging of the RY Lup disk with IRDIS (at 1.6 mu m), and obtained intensity images with the IRDIS dual-band imaging camera simultaneously with the IFS spectro-imager (0.9-1.3 mu m). Results. We resolved for the first time the scattered light from the nearly edge-on circumstellar disk around RY Lup, at projected separations in the 100 au range. The shape of the disk and its sharp features are clearly detectable at wavelengths ranging from 0.9 to 1.6 mu m. We show that the observed morphology can be interpreted as spiral arms in the disk. This interpretation is supported by in-depth numerical simulations. We also demonstrate that these features can be produced by one planet interacting with the disk. We also detect several point sources which are classified as probable background objects.