The present study synthesizes different sizes of Au nanoparticles (NPs) by adjusting the concentration of citrate. This method produces Au NPs with uniform sizes that can be used to grow Au-Ag core-shell NPs by the seeding growth method. We report the fabrication of monolayer Au NPs or Au-Ag core-shell NPs through the self-assembly of NPs on a 3-aminopropyltrimethoxysilane (APTMS)-modified silicon substrate. The results indicate that the self-assembly time of Au NPs or Au-Ag core-shell NPs plays a crucial role in determining the surface coverage of NPs on the silicon substrate. The appropriate sizes of Au NPs or Au-Ag core-shell NPs were optimized to yield the greatest SERS effect in the rhodamine B molecule. The substrates with self-assembled Au-Ag core-shell NPs can also be used to detect adenosine by a structure-switch aptamer. The combination of Au-Ag core-shell NPs and DNA-based adenosine sensors provides a facile, high enhancement, low detection limit (0.1 nM) and low cost fabrication, which shall be of significant value for practical applications of other aptamer sensing systems.