The following markup displays the pencil icon in the web browser
<asp:LinkButton
runat="server"
ID="btnRun"
ToolTip="Large String"
OnClick="btnRun_Click"
Text='<i class="fa fa-pencil-square-o" style="font-size: 24px; color: black"></i>'>
</asp:LinkButton>
<asp:LinkButton
runat="server"
ID="btnRunA"
ToolTip="Large String"
OnClick="btnRun_Click">
<i class="fa fa-pencil-square-o" style="font-size: 24px; color: black"></i>
</asp:LinkButton>
Tested in chrome, firefox and internet explorer (11).
Note how in the first asp:LinkButton the Text attribute is using single quotes.
And the second asp:LinkButton is not using the Text attribute.
Using Font Awesome 4.3.0