By studying the characteristics of binary offset carrier (BOC) autocorrelation function, an unambiguous acquisition algorithm suitable for BOC arbitrary modulation order is proposed. The BOC autocorrelation function is flipped, intercepted, and superimposed to construct a new correlation function. After adding the absolute value of the original autocorrelation function, the side peak can be completely eliminated. Theoretical analysis and simulation results show that the proposed algorithm is applicable to BOC signals with arbitrary modulation orders. By comparing the detection performance between new algorithms and other algorithms in different BOC modulation orders, under the same carrier to noise ratio, the detection probability of the new algorithm is higher; the complexity of the algorithm is low, and does not increase with the increasing modulation order; the acquisition result maintains a narrow main peak width; the discriminator output does not cause a false lock phenomenon, and the signal can be accurately tracked.