Priyatham Tadikonda Jenkins Github Plugin is not responsible for merging your PR. If your PR is successful, you can either manually merge the PR or create a script that does so. Github can notify your script to merge through a Webhook attached to pull_request event. Your script can be hosted somewhere where it can receive the request from github webhook.
https://developer.github.com/v3/activity/events/types/#pullrequestevent - Here is what the event payload can contain.
https://developer.github.com/v3/pulls/#get-if-a-pull-request-has-been-merged - Here is how to check if a PR is merged.
https://developer.github.com/webhooks/ - The `pull_request` event is triggered when a pull request is assigned, unassigned, labeled, unlabeled, opened, edited, closed, reopened, synchronize, ready_for_review , a pull request review is requested, or a review request is removed.