Unfortunately, as of the API v1.1 upgrade on June 11th 2013, twitter now only gives responses in JSON. You can view the official announcement here.
That being said, I think you may need to think broader with your google searching ;)
Within 30 seconds, I found this, and it looks like exactly what you're looking for:
RSS readers cannot subscribe to JSON feeds. twitter-json-to-rss is a set of PHP scripts that you install on your public facing server that allows you to get around this problem.
Heres the library. Note this is entirely untested by myself, so you'll have to check it out.
Basically, you need to send an authenticated request to the twitter 1.1 API, get your data, then convert the returned json to RSS for your client.
If you're using PHP, this is the fastest post to help you get up to speed with requests to the 1.1 API in PHP.