Deterministic Aperiodic (DA) arrays of gold (Au) nanoparticles are proposed as a novel approach for the engineering of reproducible surface enhanced Raman scattering (SERS) substrates. A set of DA and periodic arrays of cylindrical and triangular Au nanoparticles with diameters ranging between 50-110 nm and inter-particle separations between 25-100 nm were fabricated by e-beam lithography on quartz substrates. Using a molecular monolayer of pMA (p-mercaptoaniline) as a Raman reporter, we show that higher values of SERS enhancement factors can be achieved in DA structures compared to their periodic counterparts, and discuss the specific scaling rules of DA arrays with different morphologies. Electromagnetic field calculations based on the semi-analytical generalized Mie theory (GMT) fully support our findings and demonstrate the importance of morphology-dependent diffractive coupling (long-range interactions) for the engineering of the SERS response of DA arrays. Finally, we discuss optimization strategies based on the control of particles sizes and shapes, and we demonstrate that spatially-averaged SERS enhancement factors of the order of approximately 10(7) can be reproducibly obtained using DA arrays of Au nano-triangles. The ability to rigorously design lithographically fabricated DA arrays of metal nanoparticles enables the optimization and control of highly localized plasmonic fields for a variety of chip-scale devices, such as more reproducible SERS substrates, label-free bio-sensors and non-linear elements for nano-plasmonics.