OAuth was designed for the web with much of the protocol working through the front end. For example, the basic flow is for a client, such as a photo app, to make a request to a service, such as your photo store. Since it doesn't have permission to access your photos, the request gets redirected to you in the form of a popup. If you approve, the client gets an access token that it presents to the service. This flow doesn't sound like what you want.
There are a few extensions to OAuth that may be closer to what you want. GNAP (Grant Negotiation and Access Protocol) is one of them. It includes a lot more than you need, but the flow is through the backend, which I think is what you want.
If the overhead of digital signatures isn't a problem, you should look at zcap-ld and UCAN.