When a zero offset reference sequence is defined, the i-bit shifted sequence has phase offset i with respect to the reference sequence. In this letter, we propose a new algorithm to compute phase offsets for a periodic binary sequence using the concept of order and index of an integer based on the number theoretical approach. We define an offset evaluation function that is used to calculate the phase offset, and derive properties of the function. Once the function is computed, the phase offset of the sequence is simply obtained by taking the index of it. The new algorithm overcomes the restrictions found in conventional methods on the length and the number of '0's and '1's in binary codes. Its application to the code acquisition is also investigated to show the proposed method is useful.