Algorithms play a primary role in programming an orchestrated self-assembly of shapes into molecules. In this paper, we study the algorithmic self-assembly of squares by RNA co-transcriptional folding in its oritatami model. We formalize the square self-assembly problem in oritatami and propose a universal oritatami transcript made of 939 types of abstract molecules (beads) and of period 1294 that folds deterministically and co-transcriptionally at delay 3 and maximum arity into the n × n square modulo horizontal and vertical scaling factors for all sufficiently large n’s after building a Θ(log n) width "ruler" that measures n upon the seed of size Θ(log n) on which n is encoded in binary.