Contractile rings formed from cytoskeletal filaments mediate the division of cells. Ring formation is induced by specific crosslinkers, while contraction is typically associated with motor protein activity. Here, we engineer DNA nanotubes as mimics of cytoskeletal filaments and a synthetic crosslinker based on a peptide-functionalized starPEG construct. The crosslinker induces bundling of ten to hundred individual DNA nanotubes. Importantly, the DNA nanotube bundles curve into closed micron-scale rings in a one-pot self-assembly process yielding several thousand rings per microliter. Coarse-grained molecular dynamics simulations reproduce detailed architectural properties of the DNA rings as observed by electron microscopy. Furthermore, theory and simulations predict DNA ring contraction -- without motor proteins -- upon increasing attraction or decreasing bending rigidity of the DNA nanotubes, yielding mechanistic insights into the parameter space relevant for efficient nanotube sliding. We experimentally realize these two conditions by addition of molecular crowders or temperature increase, respectively. In agreement between simulation and experiment, we obtain ring contraction to less than half of the initial ring diameter. DNA-based contractile rings could be a future element of an artificial division machinery in synthetic cells or of contractile muscle-like materials.