When acquiring a terahertz signal from a time-domain spectroscopy system, the signal is degraded by measurement noise and the information embedded in the signal is distorted. For high-performing terahertz applications, this study proposes a method for enhancing such a noise-degraded terahertz signal using machine learning that is applied to the raw signal after acquisition. The proposed method learns a function that maps the degraded signal to the clean signal using a WaveNet-based neural network that performs multiple layers of dilated convolutions. It also includes learnable pre- and post-processing modules that automatically transform the time domain where the enhancement process operates. When training the neural network, a data augmentation scheme is adopted to tackle the issue of insufficient training data. The comparative evaluation confirms that the proposed method outperforms other baseline neural networks in terms of signal-to-noise ratio. The proposed method also performs significantly better than the averaging of multiple signals, thereby facilitating the procurement of an enhanced signal without increasing the measurement time.