It is well known that internal waves (IWs) of tidal frequency (i.e., internal tides) are successfully detected in sea surface height (SSH) by satellite altimetry. Shorter period internal solitary waves (ISWs), whose periods (and spatial scales) are an order of magnitude smaller than tidal internal waves, have been generally assumed too small to be detected with conventional altimeters. This is because conventional (pulse-limited) radar altimeter footprints are somewhat larger than or of similar size, at best, as the typical wavelengths of the ISWs. Here we demonstrate that the synthetic aperture radar altimeter (SRAL) on board the Sentinel-3A can detect short-period ISWs. A variety of signatures owing to the surface manifestations of the ISWs are apparent in the SRAL Level-2 products over the ocean. These signatures are identified in several geophysical parameters, such as radar backscatter (sigma0), sea level anomaly (SLA), and significant wave height (SWH). Radar backscatter is the primary parameter in which ISWs can be identified owing to the measurable sea surface roughness perturbations in the along-track sharpened SRAL footprint. The SRAL footprint is sufficiently small to capture radar power fluctuations over successive wave crests and troughs, which produce rough and slick surface patterns arrayed in parallel bands with scales of a few kilometers. The ISW signatures are unambiguously identified in the SRAL because of the exact synergy with OLCI (Ocean Land Colour Imager) images, which in cloud-free conditions allow clear identification of the ISWs in the sunglint OLCI images. We show that both sigma0 and SLA yield realistic estimates for routine observation of ISWs with the SRAL, which is a significant improvement from previous observations recently reported for conventional pulse-limited altimeters (Jason-2). Several case studies of ISW signatures are interpreted in light of our knowledge of radar backscatter in the internal wave field. An analysis is presented for the tropical Atlantic Ocean off the Amazon shelf to infer the frequency of the phenomena, being consistent with previous satellite observations in the study region.