Self-organization in an experimental braided river is studied. It is shown that the experimental braided river self-organizes into a critical state where it shows dynamic scaling; that is, small and large parts of the river evolve statistically identically after proper renormalization of space and time. The dynamic scaling emerges during the process of approaching the critical state which involves self-adjustment of both profile (vertical self-organization) and braiding pattern (horizontal self-organization). The obtained result corroborates the hypothesis suggested by the authors earlier [Sapozhnikov and Foufoula-Georgiou; 1997] that braided rivers are self-organized critical systems. The results are also important for understanding and statistically predicting the behavior of natural braided rivers because, owing to external conditions (e.g., sudden streamflow changes), some of them may be driven out of the critical state and therefore may show deviation from dynamic scaling.