Improving text representation has attracted much attention to achieve expressive text-to-speech (TTS). However, existing works only implicitly learn the prosody with masked token reconstruction tasks, which leads to low training efficiency and difficulty in prosody modeling. We propose CLAPSpeech, a cross-modal contrastive pre-training framework that explicitly learns the prosody variance of the same text token under different contexts. Specifically, 1) We encourage the model to connect the text context with its corresponding prosody pattern in the joint multi-modal space with the elaborate design of the encoder inputs and contrastive loss; 2) We introduce a multi-scale pre-training pipeline to capture prosody patterns in multiple levels. We show how to incorporate CLAPSpeech into existing TTS models for better prosody. Experiments on three datasets not only show that CLAPSpeech could improve the prosody prediction for existing TTS methods, but also demonstrate its generalization ability to adapt to multiple languages and multi-speaker TTS. We also deeply analyze the principle behind the performance of CLAPSpeech. Ablation studies demonstrate the necessity of each component in our method. Source code and audio samples are available at https://clapspeech.github.io.