In order to produce facial-expression-specified talking head videos, previous audio-driven one-shot talking head methods need to use a reference video with a matching speaking style (i.e., facial expressions). However, finding videos with a desired style may not be easy, potentially restricting their application. In this work, we propose an expression-controllable one-shot talking head method, dubbed TalkCLIP, where the expression in a speech is specified by the natural language. This would significantly ease the difficulty of searching for a video with a desired speaking style. Here, we first construct a text-video paired talking head dataset, in which each video has alternative prompt-alike descriptions. Specifically, our descriptions involve coarse-level emotion annotations and facial action unit (AU) based fine-grained annotations. Then, we introduce a CLIP-based style encoder that first projects natural language descriptions to the CLIP text embedding space and then aligns the textual embeddings to the representations of speaking styles. As extensive textual knowledge has been encoded by CLIP, our method can even generalize to infer a speaking style whose description has not been seen during training. Extensive experiments demonstrate that our method achieves the advanced capability of generating photo-realistic talking heads with vivid facial expressions guided by text descriptions.