The requirements for homeschooling vary significantly by state and sometimes even by county within a state. Some states require you to register your homeschool, while others require more extensive licensing or notification processes. A few states have very minimal requirements. There is no single national license required for homeschooling.
Therefore, you do not necessarily need a license, but you absolutely need to check the specific laws and regulations in your state to understand your obligations. Failing to meet the legal requirements can lead to penalties.