Cervical cancer can be prevented by having regular screenings to find any precancers and treat them. The Pap test looks for any abnormal or precancerous changes in the cells on the cervix. However, the manual screening of Pap smear in the microscope is subjective with poorly reproducible criteria. Therefore, the aim of this study was to develop a computer-assisted screening system for cervical cancer using digital image processing of Pap smear images. The analysis of Pap smear image is important in the cervical cancer screening system. There were four basic steps in our cervical cancer screening system. In cell segmentation, nuclei were detected using a shape-based iterative method, and the overlapping cytoplasm was separated using a marker-control watershed approach. In the features extraction step, three important features were extracted from the regions of segmented nuclei and cytoplasm. RF (random forest) algorithm was used as a feature selection method. In the classification stage, bagging ensemble classifier, which combined the results of five classifiers—LD (linear discriminant), SVM (support vector machine), KNN (k-nearest neighbor), boosted trees, and bagged trees—was applied. SIPaKMeD and Herlev datasets were used to prove the effectiveness of our proposed system. According to the experimental results, 98.27% accuracy in two-class classification and 94.09% accuracy in five-class classification was achieved using the SIPaKMeD dataset. When the results were compared with five classifiers, our proposed method was significantly better in two-class and five-class problems.