Create a GET Url in my custom module

I am creating a new module which is working fine. Now I need a get API to fetch data and use via jquery. Can I do that?

You can certainly call 3rd party API in your custom module and the process the response as needed.

From the core modules, Twitter, Currencies, ForecastIo are using API calls to get the data, so you could take a look at them to see how that works.