Radar emitter signal recognition under noisy background is one of the focus areas in research on radar signal processing. In this study, the soft thresholding function is embedded into deep learning network models as a novel nonlinear activation function, achieving advanced radar emitter signal recognition results. Specifically, an embedded sub-network is used to learn the threshold of soft thresholding function according to the input feature, which results in each input feature having its own independent nonlinear activation function. Compared with conventional activation functions, the soft thresholding function is characterized by flexible nonlinear conversion and the ability to obtain more discriminative features. By this way, the noise features can be flexibly filtered while retaining signal features, thus improving recognition accuracy. Under the condition of Gaussian and Laplacian noise with signal-to-noise ratio of −8 dB to −2 dB, experimental results show that the overall average accuracy of soft thresholding function reached 88.55%, which was 11.82%, 8.12%, 2.16%, and 1.46% higher than those of Sigmoid, PReLU, ReLU, ELU, and SELU, respectively.