This is the most popular (not Trusted) signed message verification website used in "Stake Bitcoin Address" thread, but it can sign as well.
It's open-source but only supports legacy p2pkh addresses.
Here's the source code so that you can use it offline and to audit as well: https://github.com/brainwalletX/brainwalletX.github.io
Online webpage Link: https://brainwalletx.github.io/#sign
You can't use QR code though, I believe message signing feature through QR should also be implemented in the wallet that'll sign to work.
It more inconvenient and doesn't have any security advantage than a simple message signing feature, so I don't think wallet developers will add such feature.