You can still use the Authorization header with OAuth 2.0. There is a Bearer type specified in the Authorization header for use with OAuth bearer tokens (meaning the client app simply has to present ("bear") the token). The value of the header is the access token the client received from the Authorization Server.
It's documented in this spec: https://tools.ietf.org/html/rfc6750#section-2.1
E.g.:
GET /resource HTTP/1.1
Host: server.example.com
Authorization: Bearer mF_9.B5f-4.1JqM
Where mF_9.B5f-4.1JqM is your OAuth access token.