AvalonEdit does not have this functionality built-in. However it provides all the infrastructure needed to implement it yourself. In the SharpDevelop IDE we have an implementation that should suit your needs.
You'll need some of the code from the SharpDevelop repository (https://github.com/icsharpcode/SharpDevelop/):
- TextMarkerService, TextMarker
- and its related interfaces and enums.
To make it easier for you, I have created a small sample application:
https://github.com/siegfriedpammer/AvalonEditSamples/tree/master/TextMarkerSample
It uses the AvalonEdit 5 nuget package and contains the classes mentioned above, plus a WPF Window to test it.