@raju Kumar , Thanks for posting this good question.
Short Answer: Leverage Azure App Service WebApps.
API Apps/WebApps are under the App Service hood- They both run on the same platform, behind the scenes.
Just to highlight on the terminology for more clarity:
App Service – Service which enables you to build and host web apps, mobile back ends, and RESTful APIs.
Apps– Your individual Apps (WebApps), these apps run in App Service Plan.
App Service Plan - An App Service plan defines a set of compute resources for a web app to run.
Kindly take a look at this tutorial - Tutorial: Host a RESTful API with CORS in Azure App Service and deployment.
Also, You may wish to know - Azure offers a number of ways to host your application code. The term compute refers to the hosting model for the computing resources that your application runs on. The flowchart in the doc, will help you to choose a compute service for your application.
- This article helps you understand the options and make the right choice for your web application.