The manual migration between different third-party libraries represents a challenge for software developers. Developers typically need to explore both libraries Application Programming Interfaces, along with reading their documentation, in order to locate the suitable mappings between replacing and replaced methods. In this paper, we introduce RAPIM, a novel machine learning approach that recommends mappings between methods from two different libraries. Our model learns from previous migrations, manually performed in mined software systems, and extracts a set of features related to the similarity between method signatures and method textual documentation. We evaluate our model using 8 popular migrations, collected from 57,447 open-source Java projects. Results show that RAPIM is able to recommend relevant library API mappings with an average accuracy score of 87%. Finally, we provide the community with an API recommendation web service that could be used to support the migration process.