Gold nanorods (AuNRs) were synthesized and optimized with the aim of obtaining strongly hydrophilic nanomaterials, suitable as a drug delivery system (DDS) for copper-based drugs. After careful purification, AuNRs were characterized by ultraviolet–visible–near-infrared spectroscopy (UV–Vis–NIR), showing two typical localized surface plasmon resonance (LSPR) bands in the range 550–750 nm. Fourier Transform Infrared (FT-IR) and high-resolution X-ray photoelectron (HR-XPS) spectroscopies verified the surface functionalization. Transmission electron microscopy (TEM) showed AuNRs with regular shape and size, with an aspect ratio (AR) of 2.6. Dynamic Light Scattering (DLS) measurements confirmed the size and the stability in water for up to 3 months. The AuNRs were conjugated with copper(I) drugs, i.e., [Cu(PTA)₄]BF₄ (PTA = 1,3,5-triaza-7-phosphadamantane). The drug loading procedures and efficiency were optimized, and the best loading was η (%) = 50 ± 7%. The non-covalent interactions of the Cu(I) complex with the AuNRs were studied by means of UV–Vis–NIR, ζ-potential, HR-TEM, FT-IR, synchrotron radiation-induced X-ray photoelectron (SR-XPS), and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy measurements. The MTT assay performed on Vero E6 cells showed that AuNRs and AuNR-Cu(I) conjugates had no significant effect on cell viability, being biocompatible, causing a reduction in cell viability only after prolonged exposure.