Erik,
from the sounds of this post you are not familiar with ArcGIS Server and Published Map Services, or I just don't understand your question. So if you have ArcGIS Server than you can take a MXD or MSD (Map Service Document) and publish them to Server using the Map Service Publishing toolbar in ArcMap for ArcGIS Server Manager. When a Map Service is published and you have Web Services installed then you can access your map service using REST endpoint just like you do ESRIs.