We propose a new dual-band passive RFID tag antenna design by combining a rectangular spiral coil and patch-meander-line dipole with an interconnected structure. This design enables operation in high-frequency (HF) and ultra-high-frequency (UHF) RFID systems, suitable for energy harvesting and tracking applications. The simulations by the CST full-wave software demonstrate conjugate impedance matching between the tag antenna and two RFID tag chips. At 13.56 MHz (HF), the tag antenna exhibits an inductive reactance of 422.79 Ω, while at 922.5 MHz (UHF), it presents an impedance of 9.41+j174.96 Ω. The antenna generates a maximum magnetic field intensity of 0.5 A/m and omnidirectional electromagnetic fields with an antenna realized gain of -4.26 dBi at 922.5 MHz. We also analyze the impact of the tag antenna combination using numerical software. Furthermore, we fabricate a prototype tag antenna and validate its performance with RFID readers. The proposed tag antenna achieves the maximum read ranges of 11 cm and 6.9 m for the HF (13.56 MHz) and UHF (920-925 MHz) bands, respectively, accompanied by the energy harvesting of 1.48 volts at the HF band by the coupling magnetic field received by the HF antenna to the chip ST25DV04K at the output voltage pin.