Long-range ordering, while typically understood as a decrease in entropy, can also be driven by increasing system entropy in certain special cases. We demonstrate that artificial spin ice arrays of single-domain nanomagnets can be designed to produce entropy-driven order. We probe thermally active tetris artificial spin ice, known to have a zero point Pauli entropy, both experimentally and through simulations. We find two-dimensional magnetic ordering in one subset of the nanomagnet moments, which we demonstrate to be induced by disorder (i.e., increased entropy) in another subset of moments. Contrasting with other entropy-driven systems, the degrees of freedom in artificial spin ice are both designable and directly observable at the microscale, and the entropy of the system is precisely calculable in simulations. This robust example, in which the system’s interactions and ground state entropy are well-defined, significantly expands the experimental landscape for the study of entropy-driven ordering.