Non-data-aided (NDA) carrier phase recovery (CPR) is one of simple CPR algorithms which simply rotates received symbols to the nearest constellation point. Unfortunately, when the NDA CPR is used with M-ary phase shift keying, it suffers inherent M-fold phase ambiguity and thus the phase ambiguity must be resolved. On the other hand, the generator matrix of polar code can be obtained with the Kronecker product of a lower triangular matrix. Hence, the Hamming weights of all columns of are given by non-negative integer powers of 2. Based on this observation, an rotationally invariant polar code suitable for digital communication systems employing binary phase shift keying and NDA CPR is proposed. The proposed polar code offers virtually identical performance under both and carrier phase offsets to that of conventional polar code with perfect CPR with identical encoding and decoding complexities.