The search for existing non-animal alternative methods for use in experiments is currently challenging because of the lack of both comprehensive structured databases and balanced keyword-based search strategies to mine unstructured textual databases. In this paper we describe 3Ranker, which is a fast, keyword-independent algorithm for finding non-animal alternative methods for use in biomedical research. The 3Ranker algorithm was created by using a machine learning approach, consisting of a Random Forest model built on a dataset of 35 million abstracts and constructed with weak supervision, followed by iterative model improvement with expert curated data. We found a satisfactory trade-off between sensitivity and specificity, with Area Under the Curve (AUC) values ranging from 0.85-0.95. Trials showed that the AI-based classifier was able to identify articles that describe potential alternatives to animal use, among the thousands of articles returned by generic PubMed queries on dermatitis and Parkinson's disease. Application of the classification models on time series data showed the earlier implementation and acceptance of Three Rs principles in the area of cosmetics and skin research, as compared to the area of neurodegenerative disease research. The 3Ranker algorithm is freely available at www.open3r.org; the future goal is to expand this framework to cover multiple research domains and to enable its broad use by researchers, policymakers, funders and ethical review boards, in order to promote the replacement of animal use in research wherever possible.