In this paper, we propose a technology for the rapid and sensitive detection of the whole viral particles of SARS-CoV-2 using double-labeled DNA aptamers as recognition elements together with the SERS method for detecting the optical response. We report on the development of a SERS-aptasensor based on a reproducible lithographic SERS substrate, featuring the combination of high speed, specificity, and ultrasensitive quantitative detection of SARS-CoV-2 virions. The sensor makes it possible to identify SARS-CoV-2 in very low concentrations (the limit of detection was 100 copies/mL), demonstrating a sensitivity level comparable to the existing diagnostic golden standard—the reverse transcription polymerase chain reaction.