To deal with the problem of carrier phase recovery in the probabilistic shaping (PS) scenarios, this paper proposed an adaptive algorithm based on statistical analysis. First, kernel density estimation was used for parameter estimation of the PS signals, and thereby the information entropy was estimated to assist the subsequent fourth-power frequency offset estimation (FOE) algorithm based on radius orientation. Then the estimated PS parameters were adopted to carry out targeted normalization of the signals for carrier phase noise recovery based on blind phase search. Furthermore, the FOE range, signal-to-noise ratio (SNR), and laser linewidth tolerance of the algorithm were simulated and analyzed. The results show that the proposed scheme can cope with different PS intensities and achieve good carrier phase recovery in a wide SNR range. In addition, compared with the carrier phase recovery algorithm for standard signals, the proposed scheme requires a shorter sliding window and has higher estimation accuracy when achieving optimal performance.