A portion of the genetic basis for many common autoimmune disorders has been uncovered by genome-wide association studies (GWAS), but GWAS do not reveal causal variants, effector genes, or the cell types impacted by disease-associated variation. We have generated 3D genomic datasets consisting of promoter-focused Capture-C, Hi-C, ATAC-seq, and RNA-seq and integrated these data with GWAS of 16 autoimmune traits to physically map disease-associated variants to the effector genes they likely regulate in 57 human cell types. These 3D maps of gene cis-regulatory architecture are highly powered to identify the cell types most likely impacted by disease-associated genetic variation compared to 1D genomic features, and tend to implicate different effector genes than eQTL approaches in the same cell types. Most of the variants implicated by these cis-regulatory architectures are highly trait-specific, but nearly half of the target genes connected to these variants are shared across multiple autoimmune disorders in multiple cell types, suggesting a high level of genetic diversity and complexity among autoimmune diseases that nonetheless converge at the level of target gene and cell type. Substantial effector gene sharing led to the common enrichment of similar biological networks across disease and cell types. However, trait-specific pathways representing potential areas for disease-specific intervention were identified. To test this, we pharmacologically validated squalene synthase, a cholesterol biosynthetic enzyme encoded by the FDFT1 gene implicated by our approach in MS and SLE, as a novel immunomodulatory drug target controlling inflammatory cytokine production by human T cells. These data represent a comprehensive resource for basic discovery of gene cis-regulatory mechanisms, and the analyses reported reveal mechanisms by which autoimmune-associated variants act to regulate gene expression, function, and pathology across multiple, distinct tissues and cell types.