To mitigate the severe impact of phase noise in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems, a goal programming-based semi-blind phase search (GP-SBPS) algorithm is proposed for probabilistically shaped CO-OFDM systems to estimate and compensate for common phase error (CPE). This algorithm sets a convergence region centered on the original constellation points after probabilistic shaping and adopts a hierarchical goal programming strategy: the first layer aims to maximize the number of signal points within the convergence region, while the second layer targets minimizing the difference in probability distribution between the compensated signals and the original constellation points. Meanwhile, it incorporates the staged test phase estimation strategy from the two-stage blind phase search (BPS) algorithm to select test phases. By comparing the objective function values derived from various test phases, the optimal test phase suitable for phase compensation is selected, thereby achieving the goal programming. Simulation results demonstrate that, compared with the traditional algorithms, the proposed algorithm can effectively suppress the common phase noise for various shaped constellations under 16-QAM and 64-QAM. It not only improves the performance of the bit error rate (BER) at the same signal-to-noise ratio (SNR) but also significantly enhances the spectral efficiency.