RNA-binding proteins (RBPs) are essential modulators of transcription and translation frequently dysregulated in cancer. We systematically interrogated RBP dependencies in human cancers using a comprehensive CRISPR/Cas9 domain-focused screen targeting RNA-binding domains of 490 classical RBPs. This uncovered a network of physically interacting RBPs upregulated in acute myeloid leukemia (AML) and crucial for maintaining RNA splicing and AML survival. Genetic or pharmacologic targeting of one key member of this network, RBM39, repressed cassette exon inclusion and promoted intron retention within mRNAs encoding HOXA9 targets as well as in other RBPs preferentially required in AML. The effects of RBM39 loss on splicing further resulted in preferential lethality of spliceosomal mutant AML, providing a strategy for treatment of AML bearing RBP splicing mutations.