Automating cytology-based cervical cancer screening could alleviate the shortage of skilled pathologists in developing countries. Up until now, computer vision experts have attempted numerous semi and fully automated approaches to address the need. Yet, these days, leveraging the astonishing accuracy and reproducibility of deep neural networks has become common among computer vision experts. In this regard, the purpose of this study is to classify single-cell Pap smear (cytology) images using pre-trained deep convolutional neural network (DCNN) image classifiers. We have fine-tuned the top ten pre-trained DCNN image classifiers and evaluated them using five class single-cell Pap smear images from SIPaKMeD dataset. The pre-trained DCNN image classifiers were selected from Keras Applications based on their top 1% accuracy. Our experimental result demonstrated that from the selected top-ten pre-trained DCNN image classifiers DenseNet169 outperformed with an average accuracy, precision, recall, and F1-score of 0.990, 0.974, 0.974, and 0.974, respectively. Moreover, it dashed the benchmark accuracy proposed by the creators of the dataset with 3.70%. Even though the size of DenseNet169 is small compared to the experimented pre-trained DCNN image classifiers, yet, it is not suitable for mobile or edge devices. Further experimentation with mobile or small-size DCNN image classifiers is required to extend the applicability of the models in real-world demands. In addition, since all experiments used the SIPaKMeD dataset, additional experiments will be needed using new datasets to enhance the generalizability of the models.