No, a database should not be an actor in a use-case diagram. A use case diagram is meant to represent the purpose of the system for its actors, independently of the system's internal structure.
The database are a component used to implement a system. So it is part of the system's internals. Actors must be external to the system.
Actors may represent independent systems that interact with your system. But some degree of autonomy is expected since they play a role in the use case: either the system actor supports the use-case, like a human actor could do, or it uses the system for achieving its own goals.
Some useful questions help to decide about candidate system actors: does the user need to know? are users or business stakeholders interested in? is the system actor a system that would be useful if your system wouldn’t exist? could we imagine the same use case with a human user instead of a system actor?