First of all, I am assuming you are trying to set a cookie for your own domain to be accessed from the same domain. You can't access a cookie across domains.
To clarify the usage of cookies, you cannot "send" a cookie with a GET request to the server.
Instead, you need to make a cookie, either sent to the client from the server, or with client-side JavaScript.
After the cookie is set, then it will automatically be included with the request to the server.
Here is a link describing cookie functions and examples of how to set one with JavaScript (as you have tagged your question): http://www.codelib.net/javascript/cookies.html