Automatic modulation recognition (AMR) technique plays an important role in the identification of modulation types of unknown signal of integrated sensing and communication (ISAC) systems. Deep neural network (DNN) based AMR is considered as a promising method. Considering the complexity of a typical ISAC system, devising the DNN manually with limited knowledge of its various classifications will be very tasking. This paper proposes a neural architecture search (NAS) based AMR method to automatically adjust the structure and parameters of DNN and find the optimal structure under the combination of training and constraints. The proposed NAS-AMR method will improve the flexibility of model search and overcome the difficulty of gradient propagation caused by the non-differentiable quantization function in the process of back propagation. Simulation results are provided to confirm that the proposed NAS-AMR method can identify the modulation types in various ISAC electromagnetic environments. Furthermore, compared with other fixed structure networks, our proposed method delivers the highest recognition accuracy, under the condition of low parameters and floating-point operations (FLOPs).