ArcMap 10.1 can do it if you have access to that. I kept an old 10.1 around for years just for this.
(This actually really caused issues for us and our developer. We were counting on it then they shut it off in 10.2 and on. Even as a Esri partner our developer got nowhere with tickets and escalation. Each dept blamed the other for turning it off and we never did get a fix or answer. )
There is another hack. If I remember right you had to add the layer to a Mosaic Dataset then cache that MD. This hides the source from ArcMap so it takes it.
Then ArcPro came along and it seems to work just fine caching a service.
Be careful though because a run away script can get you blacklisted by the Esri data host. Happened to us!
Also be aware I have 5 open bugs on the Caching tools - mostly using a AOI - for 3 years and counting now. So issues may come up. Create Tile Package is the slowest but also the most reliable.
Good luck.