Deterministic fractal antennas are employed to realize multimodal plasmonic devices. Such structures show strongly enhanced localized electromagnetic fields typically in the infrared range with a hierarchical spatial distribution. Realization of engineered fractal antennas operating in the optical regime would enable nanoplasmonic platforms for applications, such as energy harvesting, light sensing, and bio-/chemical detection. Here, we introduce a novel plasmonic multiband metamaterial based on the Sierpinski carpet (SC) space-filling fractal, having a tunable and polarization-independent optical response, which exhibits multiple resonances from the visible to mid-infrared range. We investigate gold SCs fabricated by electron-beam lithography on CaF2 and Si/SiO2 substrates. Furthermore, we demonstrate that such resonances originate from diffraction-mediated localized surface plasmons, which can be tailored in deterministic fashion by tuning the shape, size, and position of the fractal elements. Moreover, our findings illustrate that SCs with high order of complexity present a strong and hierarchically distributed electromagnetic near-field of the plasmonic modes. Therefore, engineered plasmonic SCs provide an efficient strategy for the realization of compact active devices with a strong and broadband spectral response in the visible/mid-infrared range. We take advantage of such a technology by carrying out surface enhanced Raman spectroscopy (SERS) on Brilliant Cresyl Blue molecules deposited onto plasmonic SCs. We achieve a broadband SERS enhancement factor up to 104, thereby providing a proof-of-concept application for chemical diagnostics.