No problem, you can already build such a system yourself quite trivially by getting an FTP account, mounting it locally with curlftpfs, and then using SVN or CVS on the mounted filesystem.
The modern alternative is probably Syncthing. I intermittently maintain a list of these things at https://github.com/pjc50/pjc50.github.io/blob/master/secure-... ; none of them have ever been precisely what I wanted. The cheap alternative to Dropbox with Linux support you want was "Hubic" from OVH (edit: now discontinued)
Hubic has been discontinued recently as a non-core business to OVH[1].