You cannot do this with a text box, but you can use richtextbox:
WPF RichTextBox Tutorial
var textRange = MyRichTextBox.Selection;
var start = MyRichTextBox.Document.ContentStart;
var startPos = start.GetPositionAtOffset(0);
var endPos = start.GetPositionAtOffset(1);
textRange.Select(startPos, endPos);
textRange.ApplyPropertyValue(TextElement.ForegroundProperty, new SolidColorBrush(Colors.Blue));
source
share