It seems you can easily use Heroku with svn, by using git just as a mode of transport onto Heroku.
If you've never used Heroku before, you must set up your keys and project before following the above instructions. Use the quickstart guide to get up and running in no time.
You may think that handling two version control systems is difficult, but so far I've actually found it fairly simple. Basically you treat git like you'd treat "tags" - you commit to git just before you push up to heroku.
[*] For most of my projects, I prefer having one source of truth. I've also had some rather spectacular failure-modes using git which I've not seen the like of in all my years of svn... if you're adamant on learning git, read my Number one thing to learn if new to git first...