Oracle Integration Cloud (OIC) offers a platform for building integrations between various applications, including creating REST APIs that can connect to Oracle services like an Oracle database or other cloud and on-premises applications.

To create a REST API in Oracle Integration Cloud, you typically follow these steps:

1. Design the API:
   
   1. Define the resources and operations (GET, POST, PUT, DELETE) that your API will support.
   2. You can do this by using Oracle’s API designer or by creating an OpenAPI (formerly Swagger) specification manually.
2. Implement the API:
   
   1. In OIC, navigate to the ‘Integrations’ area.
   2. Create a new Integration with the ‘App Driven Orchestration’ pattern if your API will orchestrate multiple services, or the ‘Basic Routing’ pattern if it is a simple pass-through.
   3. Define the endpoints using the REST Adapter as the trigger (for inbound connections) and as the invoke (for outbound connections) points.
   4. Map the endpoints to the operations in your application or service that you are exposing.
3. Configure Security:
   
   1. Set up the appropriate security policies for your API, such as OAuth 2.0 or Basic Auth, to ensure that only authorized clients can access it.
4. Activate and Test the Integration:
   
   1. Once your implementation is complete, activate the integration.
   2. Use a tool like Postman, or Oracle’s own test console, to test the API by making requests to the endpoints and verifying the responses.
5. Monitor and Manage the API:
   
   1. After your API is live, use OIC’s monitoring tools to track usage, performance, and errors.
   2. Manage the lifecycle of your API by versioning and retiring as necessary.
6. Document the API:
   
   1. Provide API documentation for developers who will be using your API. If you’ve created an OpenAPI specification, this can be used to generate interactive documentation that developers can use to understand how to work with your API.
7. Publish the API:
   
   1. Make the API discoverable by publishing it to your developers or a wider audience, if applicable.