In this paper, we propose a novel approach to induce automatically a Part-Of-Speech (POS) tagger for resource-poor languages (languages that have no labeled training data). This approach is based on cross-language projection of linguistic annotations from parallel corpora without the use of word alignment information. Our approach does not assume any knowledge about foreign languages, making it applicable to a wide range of resource-poor languages. We use Recurrent Neural Networks (RNNs) as multilingual analysis tool. Our approach combined with a basic cross-lingual projection method (using word alignment information) achieves comparable results to the state-of-the-art. We also use our approach in a weakly supervised context, and it shows an excellent potential for very low-resource settings (less than 1k training utterances).