Yes! As of 1.7.10, you can upload your single player world to Minecraft Realms. The non-obvious bit is that you need to create a world in Minecraft Realms first, then overwrite it with your single-player world.
First create a worldin Minecraft Realms:
- Load Minecraft
- Click "Minecraft Realms"
- Click "Create World"
Once you have a world in Minecraft Realms, here is how to overwrite it with your single-player world:
- Load Minecraft
- Click "Minecraft Realms"
- Click your Realms world
- Click "Configure"
- Click "Edit World"
- Click "Upload world"
- Click the world you world you want to upload
- Click "Upload"