You sure can, here's how:

1. Download and install FileZilla Client -- it's easy, Google can help you here!
2. Go to the Servers page on our control panel, click on Manage for your server, and click on the SFTP tab. The credentials will have a "copy to clipboard" button beside them.
3. Stop your arkservers.io server.
4. Find the source folder that you'll be copying save files from. This will be C:\Program Files (x86)\Steam\steamapps\common\ARK\ShooterGame\Saved\SavedArksLocal on Windows. On Linux, it'll be something ending in ShooterGame/Saved/SavedArks.
5. Navigate to the remote folder /arkserver/ShooterGame/Saved/SavedArks and delete everything in that folder.
6. Copy all files from the source folder to /arkserver/ShooterGame/Saved/SavedArks.
7. When copying from a local server, some files will start with LocalPlayer. Files starting with LocalPlayer need to have the word "LocalPlayer" replaced with your steam id. To get your steam id, login to store.steampowered.com in your browser, navigate to your profile, and look at the id in the URL.
8. You cannot upload ini files, so you'll need to configure your settings and mods all over again (mods can be searched for by mod ID). Fortunately, our awesome control panel makes this easy!
9. Start your arkservers.io server up, giving time for the mods to download and fully install, and enjoy your new server!