Can I convert my C++ Basic project to VR?

I have created simple games with C++ / Basic / Starter content. If I would like to run them in VR (Oculus on Windows) I need to add support for moving around and grabbing things of course. But can I convert the project I have to a VR project in Unreal, or maybe that’s a silly question?

The VR template when starting a new project is only available on the Blueprint tab and not the VR tab.

Yes, you can. Just the C++ project is designed in VR mode with VR modules/plugins (SteamVR, Oculus, OpenVR, etc).