Most studies of genome organization have focused on intra-chromosomal (cis) contacts because they harbor key features such as DNA loops and topologically associating domains. Inter-chromosomal (trans) contacts have received much less attention, and tools for interrogating potential biologically relevant trans structures are lacking. Here, we develop a computational framework to identify sets of loci that jointly interact in trans from Hi-C data. This method, trans-C, initiates probabilistic random walks with restarts from a set of seed loci to traverse an input Hi-C contact network, thereby identifying sets of trans-contacting loci. We validate trans-C in three increasingly complex models of established trans contacts: the Plasmodium falciparum var genes, the mouse olfactory receptor "Greek islands", and the human RBM20 cardiac splicing factory. We then apply trans-C to systematically test the hypothesis that genes co-regulated by the same trans-acting element (i.e., a transcription or splicing factor) co-localize in three dimensions to form "RNA factories" that maximize the efficiency and accuracy of RNA biogenesis. We find that many loci with multiple binding sites of the same transcription factor interact with one another in trans, especially those bound by transcription factors with intrinsically disordered domains. Similarly, clustered binding of a subset of RNA binding proteins correlates with trans interaction of the encoding loci. These findings support the existence of trans interacting chromatin domains (TIDs) driven by RNA biogenesis. Trans-C provides an efficient computational framework for studying these and other types of trans interactions, empowering studies of a poorly understood aspect of genome architecture.