I want to implement video calling in my android application. What is best option for implementing this application?
Definitely i would recommend
WebRTC (Web Real time Communication)
it's a free, open project that provides browsers and mobile applications with Real-Time Communications (RTC) capabilities via simple APIs. The WebRTC components have been optimized to best serve this purpose.
Here's an android app sample using it. ( i tried it myself)
https://github.com/RWebRTC/WebRTC-Android-Learn
And this is the official webRTC website: https://webrtc.org
And if you are willing to use a paid but fast to integrate service i would recommend Sinch: https://www.sinch.com/