Using the Authorization header seems like the right thing to do. It's the entire purpose of the Authorization header.
From http://tools.ietf.org/html/rfc7235#section-4.2https://www.rfc-editor.org/rfc/rfc7235#section-4.2 :
The "Authorization" header field allows a user agent to authenticate itself with an origin server -- usually, but not necessarily, after receiving a 401 (Unauthorized) response. Its value consists of credentials containing the authentication information of the user agent for the realm of the resource being requested.
If you have your own auth scheme document it, but there's no need to reinvent the wheel.