The endomorphism ring End(A) of an abelian variety A is an order in a semi-simple algebra over Q. The co-index of End(A) is the index to any maximal order containing it. We show that for abelian varieties of fixed dimension over any field of characteristic p>0, the p-exponents of the co-indices of their endomorphism rings are bounded. This gives a constraint for which order of a finite-dimensional semi-simple Q-algebras that can be the endomorphism ring of an abelian variety of positive characteristic.