An easy desktop would be to forget Borderin your xaml and use TextBoxinstead TextBlockas follows:
<TextBox Text="Your Text Here"
IsReadOnly="True" Background="Transparent" BorderBrush="Red"
BorderThickness="3" HorizontalAlignment="Left"/>
UPDATE:
I checked again and it looks like you forgot to set BorderHorizontalAlignment
This also works:
<Border CornerRadius="5" HorizontalAlignment="Left" BorderThickness="10">
<TextBlock Text="My Text Here"></TextBlock>
</Border>
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