Decades of work have aimed to genetically reprogram T cells for therapeutic purposes^1,2 using recombinant viral vectors, which do not target transgenes to specific genomic sites^3,4. The need for viral vectors has slowed down research and clinical use as their manufacturing and testing is lengthy and expensive. Genome editing brought the promise of specific and efficient insertion of large transgenes into target cells using homology-directed repair^5,6. Here we developed a CRISPR-Cas9 genome-targeting system that does not require viral vectors, allowing rapid and efficient insertion of large DNA sequences (greater than one kilobase) at specific sites in the genomes of primary human T cells, while preserving cell viability and function. This permits individual or multiplexed modification of endogenous genes. First, we applied this strategy to correct a pathogenic IL2RA mutation in cells from patients with monogenic autoimmune disease, and demonstrate improved signalling function. Second, we replaced the endogenous T cell receptor (TCR) locus with a new TCR that redirected T cells to a cancer antigen. The resulting TCR-engineered T cells specifically recognized tumour antigens and mounted productive anti-tumour cell responses in vitro and in vivo. Together, these studies provide preclinical evidence that non-viral genome targeting can enable rapid and flexible experimental manipulation and therapeutic engineering of primary human immune cells.