Securing low-power Internet-of-Things (IoT) sensor nodes is a critical challenge for the widespread adoption of IoT technology due to their limited energy, computation, and storage resources. As an alternative to the traditional wireless security solution based on cryptography, there has been growing interest in RF physical-layer security, which promises a lower overhead and energy cost. In this work, we demonstrate energy-efficient physical-layer identification, a.k.a., RF fingerprinting, designed specifically for resource-constrained IoT nodes. To enhance the identification performance beyond prior demonstrations using off-the-shelf radios, we propose a minor modification to the radio frontend by integrating a digital physically unclonable function (PUF). The PUF controls the transmitter (TX) spectral regrowth as the RF fingerprint (RFF), enhancing its uniqueness and identification space beyond solely relying on transistor intrinsic process variations. As a proof of concept, a 2.4-GHz physical-layer identification is implemented in the GlobalFoundries 45-nm CMOS SOI process. It achieves 4.7-dBm output power and 36% efficiency, which are comparable to state-of-the-art low-power 2.4-GHz power amplifiers (PAs). Additionally, it demonstrates significant improvement in RFF reliability, uniqueness, and identification space over prior physical-layer identification demonstrations. The identification rate and security performance of the proposed approach under different attack models are also discussed.