Ants feed off the honeydew produced by the aphids, so getting rid of one should reduce the other. Can you follow the ants' trails back to their nest(s) and destroy them with boiling water, and/or spray the aphids with a soap solution (in my experience cats avoid soap so shoudn't be affected)?

Xela's right - you need to check the tree for either aphid or scale insect infestation - the likeliest is aphid. Get rid of these, and the ants will disappear.