Open the solution in Visual Studio 2013 and Select File and Add this to Source Control
Then Select the Microsoft Git Provider. That will create a local GIT repository
Surf the repository to GitHub.
Now you need to create a new repository and Initialize this repository with a README
Then it will create an empty repository without a Master branch.
Open the repository and copy the URL. Then go back to Visual Studio
Make sure that you have the Microsoft Git Provider selected under:
Tools/Options/Source Control/Plug-in Selection
Now Open Team Explorer
And select Home and Unsynced Commits
Enter the GitHub URL into the box.
Then click on Publish
Select Home and add Changes then commit it with a comment.
Select Commit and Push
This process will help you to add your existing solution to github from visual-studio-2013.