Nucleotide variants can cause functional changes by altering protein-RNA binding in various ways that are not easy to predict. This can affect processes such as splicing, nuclear shuttling, and stability of the transcript. Therefore, correct modeling of protein-RNA binding is critical when predicting the effects of sequence variations. Many RNA-binding proteins recognize a diverse set of motifs and binding is typically also dependent on the genomic context, making this task particularly challenging. Here, we present DeepCLIP, the first method for context-aware modeling and predicting protein binding to RNA nucleic acids using exclusively sequence data as input. We show that DeepCLIP outperforms existing methods for modeling RNA-protein binding. Importantly, we demonstrate that DeepCLIP predictions correlate with the functional outcomes of nucleotide variants in independent wet lab experiments. Furthermore, we show how DeepCLIP binding profiles can be used in the design of therapeutically relevant antisense oligonucleotides, and to uncover possible position-dependent regulation in a tissue-specific manner. DeepCLIP is freely available as a stand-alone application and as a webtool at http://deepclip.compbio.sdu.dk.