Biology provides numerous examples of self-replicating machines, but artificially engineering such complex systems remains a formidable challenge. In particular, although simple artificial self-replicating systems including wooden blocks, magnetic systems, modular robots and synthetic molecular systems have been devised, such kinematic self-replicators are rare compared with examples of theoretical cellular self-replication. One of the principal reasons for this is the amount of complexity that arises when you try to incorporate self-replication into a physical medium. In this regard, DNA is a prime candidate material for constructing self-replicating systems due to its ability to self-assemble through molecular recognition. Here, we show that DNA T-motifs, which self-assemble into ring structures, can be designed to self-replicate through toehold-mediated strand displacement reactions. The inherent design of these rings allows the population dynamics of the systems to be controlled. We also analyse the replication scheme within a universal framework of self-replication and derive a quantitative metric of the self-replicability of the rings.