API [API]
NOUN
computing
a set of functions and procedures allowing the creation of applications that access the features or data of an operating system, application, or other service.
TLDR; yes, but it is hard.
Big Giants
Unless you have a very specific domains that could generate lots of interests, most applications that could be generating incomes are in high competitions. For example, in the domain of storage, we have Amazon S3.
APIs are not enough
Even if you find such applications, providing APIs alone are not enough. You will need a UI/dashboard for developers to monitor/access the statistics/APIs. You will also need to scale your APIs at some point.
I have developed some APIs. And only one of them was making some revenues in the past.