We demonstrate an intense broadband terahertz (THz) source based on the interaction of relativistic-intensity femtosecond lasers with aligned copper nanorod array targets. For copper nanorod targets with a length of 5 μm, a maximum 13.8 times enhancement in the THz pulse energy (in ≤20 THz spectral range) is measured as compared to that with a thick plane copper target under the same laser conditions. A further increase in the nanorod length leads to a decrease in the THz pulse energy at medium frequencies (≤20 THz) and increase of the electromagnetic pulse energy in the high-frequency range (from 20-200 THz). For the latter, we measure a maximum energy enhancement of 28 times for the nanorod targets with a length of 60 μm. Particle-in-cell simulations reveal that THz pulses are mostly generated by coherent transition radiation of laser produced hot electrons, which are efficiently enhanced with the use of nanorod targets. Good agreement is found between the simulation and experimental results.