  We give a mathematically rigorous construction of a magnetic Schr\"odinger
operator corresponding to a field with flux through finitely many holes of the
Sierpinski Gasket. The operator is shown to have discrete spectrum accumulating
at $\infty$, and it is shown that the asymptotic distribution of eigenvalues is
the same as that for the Laplacian. Most eigenfunctions may be computed using
gauge transformations corresponding to the magnetic field and the remainder of
the spectrum may be approximated to arbitrary precision by using a sequence of
approximations by magnetic operators on finite graphs.
