There are several structural design patterns that can be used for API integration in C#, but the best one for you will depend on the specifics of your project. Here are a few common options:

1. Adapter pattern: This pattern allows you to convert the interface of a class into another interface that the client expects. This can be useful when you need to integrate with an API that has a different interface than what your client code expects.
2. Facade pattern: This pattern provides a simplified interface to a complex system. If your API integration involves accessing multiple APIs, this pattern can be useful for simplifying the overall interface for the client code.
3. Decorator pattern: This pattern allows you to dynamically add behavior to an object without affecting other objects from the same class. This can be useful for adding additional functionality to the API integration, such as logging or error handling.
4. Observer pattern: This pattern allows you to create a one-to-many relationship between objects, so that when one object changes state, all its dependants are notified and updated automatically. This can be useful for integrating with an API that sends notifications or updates.

Ultimately, the best pattern to use will depend on the specific requirements of your project and the API you are integrating with. It’s important to carefully consider the trade-offs between different patterns before making a choice.