Hi @A.Anu Manasa - do you really want to deploy straight from source control to Edge without running any CI process in the middle, i.e. testing, configuration management, etc?
I'd strongly urge you to consider a CI process which automatically picks up new commits in a specific branch, run code analysis, unit tests, deploy code to Apigee and run integration/smoke tests, etc...
Have a look at this presentation for CI process for Apigee proxies: http://www.slideshare.net/apigee/i-love-apis-2015-continuous-integration-the-virtuous-cycle
PS: Answer to your original question is no - there is no way for you to deploy api proxies straight from github.
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