The distribution of potential, electric field, and gradient of square of electric field was simulated via a finite element method for dielectrophoresis (DEP) assembly. Then reduced graphene oxide sheets (RGOS)- and graphene oxide sheets (GOS)-based electrical circuits were fabricated via DEP assembly. The mechanically exfoliated graphene sheets (MEGS)-based electrical circuit was also fabricated for comparison. The electrical transport properties of three types of graphene-based electrical circuits were measured. The MEGS-based electrical circuit possesses the best electrical conductivity, and the GOS-based electrical circuit has the poorest electrical conductivity among all three circuits. The three types of electrical circuits were applied for the detection of copper ions (Cu2+). The RGOS-based electrical circuit can detect the Cu2+ when the concentration of Cu2+ was as low as 10 nM in solution. The GOS-based electrical circuit can only detect Cu2+ after chemical reduction. The possible mechanism of electron transfer was proposed for the detection. The facile fabrication method and excellent performance imply the RGOS- based electrical circuit has great potential to be applied to metal ion sensors.