In this work, we report the synthesis of a new double-stranded copper(I) helicate (H) and its use for the first time in a single-walled carbon nanotube-modified screen printed electrode (SWCNT/SPCE) for the voltammetric determination of amaranth (AM) and tartrazine (TZ). H was synthesized through a self-assembly process between Cu(I) iodide and 1,3-bis(1H-benzotriazol-1-ylcarbonyl)benzene (L). The compound was structurally characterized by infrared, photoluminescence spectroscopy, elemental and thermogravimetric analyses as well as single-crystal and powder X-ray diffraction. The SWCNT/SPCE was coated with H by simple drop casting, and the surface (H-SWCNT/SPCE) was characterized using cyclic voltammetry, electrochemical impedance spectroscopy (EIS) and Raman spectroscopy. The presence of H on the surface of the modified electrode reduces the charge transfer resistance of the redox couple and improves the sensitivity toward the oxidation of AM and TZ with oxidation current increases of almost 80% and 60%, respectively, thus allowing their determination using square-wave adsorptive stripping voltammetry (SWAdSV). The detection limits (3σ/b) were 30.0 and 60.0 nmol L−1 for AM and TZ, respectively. The relative standard derivation was 3.5% (n = 7) with three different electrodes. Furthermore, the new sensor was applied in the detection of these dyes in commercial samples such as synthetic orange juice and a soft drink.