Motivated by the theory of fractal strings and complex dimensions of M. L. Lapidus and M. van Frankenhuijsen, we define a class of fractal strings for self-similar measures based on scaling regularity. In turn, these fractal strings allow for an analysis of the symbolic dynamics on such measures via the abscissae of convergence of scaling zeta functions. With this approach, we recover (among other things) Moran's theorem regarding the Hausdorff dimension of self-similar sets and the Hausdorff dimensions of Besicovitch subsets.