With the rapid increase of wireless connectivity, current spectrum resources are not enough for significant requirements for large data capacity. Research interests are moving towards the high-frequency band in the terahertz range for wider bandwidth. However, multipath scattering and induced time delay, suffered by terahertz links propagating in outdoor weather, lead inevitably to increasing expenses in baseband signal processing. This trades away the advantage of low time latency and high stability, which are commonly considered as important merits of terahertz wireless communication techniques. To reduce the burden in signal processing and explore the feasibility of modulation identification in the terahertz band, a method of wireless link modulation identification is considered as a potential solution. In this work, it is investigated theoretically by employing two kinds of neural networks: the convolutional neural network (CNN) and the long short-term memory network (LSTM). Link deterioration caused by different atmospheric weather is introduced into the theoretical model, and the performance of this method is evaluated. Results show that the identification accuracy of the constructed neural networks can be up to 99%, which means such a method is efficient for identification of the modulation format of terahertz wireless links under different weather conditions. This work demonstrates the feasibility of modulation identification in outdoor terahertz communication scenarios and provides specific references.