well, when you say the object has aquired a positive charge, I'll assume you mean that it has lost electrons to another object or to ground....therefore ever so slightly reducing its mass...if it then aquires negative charge, it has ever so slightly gained mass through the addition of electrons to the object
but.....this is going to be negligable in almost sny real world case
I'm a physicist going for a doctorate, so throw me a little more info about the problem and I'll shoot for a little more detail!