  We discuss the Schr\"odinger functional in lattice QCD with staggered
fermions including its order $O(a)$ boundary counterterms. We relate it, in the
classical continuum limit, to the Schr\"odinger functional as obtained in the
same limit with Wilson fermions. We compute the strong coupling constant
defined via the Schr\"odinger functional with staggered fermions at one loop
and show that it agrees with the continuum running coupling constant in the
Schr\"odinger functional formalism.
