I want o to develope an application using cloudant API. There is documentation for creating REST application using Phalcon PHP. But how to REST API of third party.
Phalcon does not provides any classes for interaction with remote REST services or the Cloudant API. There is currently one pull request for adding different HTTP clients, which would allow you to build your own interfaces with Phalcon for specific services.
As long as Phalcon don't provides this feature you can use the standard PHP HTTP client functions using the curl extension or stream wrappers.