you might have more luck if you summer bud graft a bud onto another apple tree. the following is from an apple tree site here in Canada. I have been bud grafting onto existing apple trees, I have not had any success trying to root an apple branch and it is my understanding that the branch needs to be dormant and then cold stored to callus over.

Budding:
The grower buys rootstocks in the spring and plants them in their nursery. During the first summer, a bud is taken from a tree of the variety of apple tree that the grower wants to reproduce. (The bud is a very small piece of the tree that would grow into leaves and blossoms the following spring. They are found just where a leaf is attached to a branch.) The grower then makes a small cut in the bark of the rootstock about a foot (30 cm) up from the ground. The bud is then carefully slipped into the the cut (i.e., under the bark). The cut in the tree is then wrapped tightly with an elastic band; however, the grower is careful not to cover the bud. The next spring, the bud begins to grow and becomes a shoot growing out from the side of the rootstock.