Frequency diversity array (FDA) radar can provide full spatial coverage with stable gains within a pulse duration. Based on the FDA, the integrated radar‐communication system can perform multi‐directional communication and whole‐space detection. However, the embedded communication bits disrupt the correlation of the transmitting waveform of each element. Correspondingly, the range sidelobe level (SLL) of the multi‐dimensional ambiguity function increases significantly. To address this issue, a low‐sidelobe waveform for integrated radar‐communication systems based on the FDA was designed. Two techniques based on the subarray time delay are employed to reduce the SLL in range dimension. Both methods, however, lower the angular resolution. Thus, a tangent FM signal as the baseband waveform to improve the angular resolution was selected. Simultaneously, the received signal processing methods of radar and communication was designed. The performances of the designed waveform are verified by analysing the multi‐dimensional ambiguity function and the bit error rate. The simulation results reveal that the proposed method can maintain a good radar target detection capability and satisfy the communication function.