There is not one universal federal “perfume oil license” that every U.S. fragrance seller applies for.
Perfume intended to make a person smell good is generally regulated as a cosmetic by the FDA. Businesses are still responsible for cosmetic safety, labeling and any other requirements that apply to them. MoCRA also created requirements involving areas such as facility registration and product listing, although certain small businesses may qualify for exemptions.
Business licensing is separate. State, county and city requirements depend on where and how the business operates, and the SBA recommends checking the requirements for the specific business location and activity.
So the answer is not simply yes or no.
If you plan to sell perfume oils, check both cosmetic regulations and your state and local business requirements before launching.