Complex-field signal recovery problems from noisy linear/nonlinear measurements appear in many areas of signal processing and wireless communications. In this paper, we propose a trainable iterative signal recovery algorithm named complex-field TISTA (C-TISTA) which treats complex-field nonlinear inverse problems. C-TISTA is based on the concept of deep unfolding and consists of a gradient descent step with the Wirtinger derivatives followed by a shrinkage step with a trainable complex-valued shrinkage function. Importantly, it contains a small number of trainable parameters so that its training process can be executed efficiently. Numerical results indicate that C-TISTA shows remarkable signal recovery performance compared with existing algorithms.