Many of the members of the Justice League had a choice for getting their abilities and powers, or when to use them. Victor Stone did not. After an explosion caused his father to do experimental surgery with alien tech to save his life, Victor Stone was gone, and Cyborg was born.
Despite this, Cyborg would become a member of the League, and would help them save the world numerous times. For Batman, Cyborg, though technically the "rookie" of the bunch, is an incredible asset, one he fully appreciates. Cyborg is plugged into every computer in the world, he records everything he sees and hears, and can even create boom tubes to other places.
Batman often uses Cyborg to help with his detective work when he's around. Or, if there's a piece of tech he doesn't understand, rare as that may be, he'll call in Cyborg for a second opinion.
Batman is also one who treats him like a person, and not just as a cyborg.