Recently, the low earth orbit satellite communications has been attracting much attention. These communications have many strong features, however, the communication performances are influenced by carrier frequency offset (CFO) and, particularly, it is hard to acquire the synchronization. A large number of publications have so far been made on the synchronization acquisition of DS/SS systems under CFO and most of them make use of the maximum likelihood decision in finding the maximum values of Fourier transform outputs. However, the implementations of Fourier transforms usually require high cost and large space. In this paper, we propose a new simple acquisition scheme using half-symbol differential decoding technique for DS/SS systems under CFO. This scheme makes use of the addition and subtraction of baseband signals and their delayed versions, (omitting Fourier transforms), together with integrations by recursive integrators, and thus resulting in much simpler implementation. In general, it is shown that the proposed scheme can acquire the code synchronization under carrier frequency offset with much smaller computational complexities and the sacrifice of longer acquisition time.