Text sentiment classification is a challenge research topic in natural language processing. Lexicon-based methods and traditional machine learning-based methods rely on high-quality sentiment lexicon and robust feature engineering respectively, whereas most deep learning methods are heavily reliant on large human-annotated data sets. Fortunately, users on various social platforms generate massive amounts of tagged opinioned texts which can be deemed as weakly-labeled data for sentiment classification. However, noisy labeled instances in weakly-labeled data have a negative impact on the training phase. In this paper, we present a weakly-supervised contrastive learning framework for few-shot sentiment classification that learns the sentiment semantics from large user-tagged data with noisy labels while also exploiting inter-class contrastive patterns hidden in small labeled data. The framework consists of two steps: first, we design a weakly-supervised pre-training strategy to reduce the influence of the noisy labeled samples, and then the contrastive strategy is used in supervised fine-tuning to capture the contrast patterns in the small labeled data. The experimental results on Amazon review data set show that our approach outperforms the other baseline methods. When fine-tuned on only 0.5% (i.e. 32 samples) of the labels, we achieve comparable performance among the deep baselines, showing its robustness in the data sparsity scenario.