This work presents a novel spectral sensing method for the detection of signals presenting nonlinear phase variation over time. The introduced method is based on the angle-time cyclostationarity theory, which applies transformations to the signal to be sensed in order to mitigate the effects of nonlinear phase variation. The architecture is employed for sensing binary phase shift keying (BPSK) signals, being also compared with time cyclostationarity. The obtained simulation results clearly demonstrate the efficiency of the proposed approach, while presenting improved performance in terms of the detection rate of primary users increased by about 8 dB.