First, have you tried adjusting the sliding dropouts? It's easy to get this kind of misalignment when one side (right, in your case) is further back than the other.

If the frame is fine, you might want to re-space the hub (requires cone wrenches) or pull the rim over to the non-drive side (requires a spoke wrench). Go for the first option if the wheel is already pretty true. If it's not, then you might as well true it while you adjust the left-right alignment.

Because both of your frames use the same 135 mm spacing, I would be wary of using a spacer.