My daughter is 15 yrs old, her biological father was put on child support about 3 yrs ago. He recently married and started encouraging my daughter that he wants to start raising her. We live in two different states and this is causing a lot of issues in my household. Since I will not let her move, is there anything he can do without my constent within the law that will let her move in with him and his new family?

No, she is not an adult and he would need a Court Order before she can live with him UNLESS you consent.

At 15 her interest may be considered in a court of law. So in that respect if he takes it to court and there is reason enough to compell a change in custody then doesn't matter if you agree or not it will happen.

I will assume you are the custodial parent and have legal custody though the court. With that assumption, she can not go unless you let her, or unless he goes back to court for a change in custody.