Most works on computational morality focus on moral polarity recognition, i.e., distinguishing right from wrong. However, a discrete polarity label is not informative enough to reflect morality as it does not contain any degree or intensity information. Existing approaches to compute moral intensity are limited to word-level measurement and heavily rely on human labelling. In this paper, we propose MoralScore, a weakly-supervised framework that can automatically measure moral intensity from text. It only needs moral polarity labels, which are more robust and easier to acquire. Besides, the framework can capture latent moral information not only from words but also from sentence-level semantics which can provide a more comprehensive measurement. To evaluate the performance of our method, we introduce a set of evaluation metrics and conduct extensive experiments. Results show that our method achieves good performance on both automatic and human evaluations.