Final answer:
Prior Appropriation Rights are the type of rights acquired by diverting water and using it for a specified period of time specified by statute.
Step-by-step explanation:
The type of rights acquired by diverting water and putting it to use for a specified period of time specified by statute is Prior Appropriation Rights. Prior Appropriation Rights are a legal framework that allows individuals to claim rights over water by being the first to use it for a beneficial purpose. These rights are commonly used in areas with limited water resources, such as the western United States.