Inspired by excellent precision of carrier phase positioning, this paper presents a new carrier phase positioning technique for 5G new radio cellular networks with a focus on clock synchronization and integer ambiguity resolution. A carrier-phase based clock offset estimation method is first proposed to achieve precise clock synchronization among base stations, and proved to achieve the Cramér-Rao Lower Bound (CRLB) asymptotically. A fusion method is developed to fuse the estimated positions of a mobile station (MS) based on time-difference-of-arrival, with the estimated position changes based on the temporal changes of carrier phase measurements. While circumventing the integer ambiguities of the carrier phase measurements, the fusion method provides quality interim estimates of the MS positions, at which the measurements can be linearized to resolve the integer ambiguities. As a result, precise MS positions can be obtained based on the disambiguated carrier phase measurements. Numerical simulations show that the proposed carrier phase positioning can achieve a centimeterlevel accuracy in wireless cellular networks.