High-precision positioning accuracy is among the key features of the future fifth-generation (5G-advanced) cellular networks to enable a wide variety of commercial, critical, and consumer use cases. 5G new radio (NR) systems have relied on (1) cellular temporal/angular-based positioning methods to provide the indoor environments with a moderate positioning accuracy that is well below the positioning requirements of these future use cases and (2) highly precise satellite carrier phase/code-based positioning methods for the outdoor deployments that are limited by the availability of the satellite coverage. This paper defines the relevant standard mechanisms and algorithms to use the carrier phase cellular-based measurements as a potential solution to achieve a high-precision positioning estimation accuracy in 5G-advanced NR networks. The presented positioning technique is evaluated using high-fidelity system-level simulations for indoor factory (InF) deployment scenarios. The numerical results demonstrate that the presented technique can significantly improve the positioning accuracy compared with the state-of-the-art NR positioning methods. Our findings in this paper also show that the carrier phase method not only provides an indoor complement to the outdoor satellite positioning but also provides an outdoor alternative to the high-precision satellite methods.