If a rotor is bad will that turn your abs light on?

That's not very likely. Also would need more info on the vehicle to tell you what is possibly wrong with it.

It could be a fuse,

Could be a wheel speed sensor, with front wheels removed you will see a hose, which is your brake line, and goes to your brake caliper, and a wire, which goes into hub/spindle. This is the wheel speed sensor for the ABS. From time to time they get covered with brake dust and need to be cleaned off. There is one sensor on each side of the front of the car. If this doesn't solve your problem, you need to have your car checked for the trouble code so you don't waste money on un needed items.