The ring-shaped structural maintenance of chromosome (SMC) complexes are multi-subunit ATPases that topologically encircle DNA. SMC rings make vital contributions to numerous chromosomal functions, including mitotic chromosome condensation, sister chromatid cohesion, DNA repair, and transcriptional regulation. They are thought to do so by establishing interactions between more than one DNA. Here, we demonstrate DNA-DNA tethering by the purified fission yeast cohesin complex. DNA-bound cohesin efficiently and topologically captures a second DNA, but only if that is single-stranded DNA (ssDNA). Like initial double-stranded DNA (dsDNA) embrace, second ssDNA capture is ATP-dependent, and it strictly requires the cohesin loader complex. Second-ssDNA capture is relatively labile but is converted into stable dsDNA-dsDNA cohesion through DNA synthesis. Our study illustrates second-DNA capture by an SMC complex and provides a molecular model for the establishment of sister chromatid cohesion.