Cervical abnormal cell detection plays a crucial role in the early screening of cervical cancer. In recent years, some deep learning-based methods have been proposed. However, these methods rely heavily on large amounts of annotated images, which are time-consuming and labor-intensive to acquire, thus limiting the detection performance. In this paper, we present a novel Semi-supervised Cervical Abnormal Cell detector (SCAC), which effectively utilizes the abundant unlabeled data. We utilize Transformer as the backbone of SCAC to capture long-range dependencies to mimic the diagnostic process of pathologists. In addition, in SCAC, we design a Unified Strong and Weak Augment strategy (USWA) that unifies two data augmentation pipelines, implementing consistent regularization in semi-supervised learning and enhancing the diversity of the training data. We also develop a Global Attention Feature Pyramid Network (GAFPN), which utilizes the attention mechanism to better extract multi-scale features from cervical cytology images. Notably, we have created an unlabeled cervical cytology image dataset, which can be leveraged by semi-supervised learning to enhance detection accuracy. To the best of our knowledge, this is the first publicly available large unlabeled cervical cytology image dataset. By combining this dataset with two publicly available annotated datasets, we demonstrate that SCAC outperforms other existing methods, achieving state-of-the-art performance. Additionally, comprehensive ablation studies are conducted to validate the effectiveness of USWA and GAFPN. These promising results highlight the capability of SCAC to achieve high diagnostic accuracy and extensive clinical applications.