It is so simple.You just have to Enable the RichTextBox ‘s property “SpellCheck.IsEnabled” to True.
· XAML code for RichTextBox Control
<Window x:Class="MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="MainWindow" Height="350" Width="525">
<RichTextBox Height="100" SpellCheck.IsEnabled="True" Name="RichTextBox1" Width="200" />
</Window>