The programmable assembly of DNA strands is a promising tool for building tailored bottom-up nanostructures. Here, we present a plasmonic nanosystem obtained by the base-pairing mediated aggregation of gold nanoparticles (NPs) which are separately functionalized with two different single-stranded DNA chains. Their controlled assembly is mediated by a complementary DNA bridge sequence. We monitor the formation of DNA assembled NP aggregates in solution, and we study their Surface Enhanced Raman Scattering (SERS) response by comparison with the single NP constituents. We interpret the revealed SERS signatures in terms of the molecular and NP organization at the nanoscale, demonstrating that the action of the DNA bridge molecule yields regular NP aggregates with controlled interparticle distance and reproducible SERS response. This demonstrates the potential of the present system as a stable, biocompatible, and recyclable SERS sensor.