Have you tried to set the TopIndex property?
listBox.TopIndex = itemIndex;
Sorry, my first understanding of your question was completely wrong. I think you can do it by using javascript. I tested the sample below on Windows 7 and IE8 and it worked.
<%@ Page Language="C#" AutoEventWireup="true" CodeFile="Default.aspx.cs" Inherits="_Default" %>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
<title></title>
<script type="text/javascript">
function setSelectedIndex() {
var listBox = $get('listBox');
var textBox = $get('textBox');
listBox.selectedIndex = textBox.value;
}
</script>
</head>
<body>
<form id="form1" runat="server">
<div>
<asp:ScriptManager ID="ScriptManager1" runat="server">
</asp:ScriptManager>
<asp:ListBox runat="server" ID="listBox">
<asp:ListItem Text="A" Value="A" />
<asp:ListItem Text="B" Value="B" />
<asp:ListItem Text="C" Value="C" />
<asp:ListItem Text="D" Value="D" />
<asp:ListItem Text="E" Value="E" />
<asp:ListItem Text="F" Value="F" />
<asp:ListItem Text="G" Value="G" />
<asp:ListItem Text="H" Value="H" />
<asp:ListItem Text="I" Value="I" />
<asp:ListItem Text="K" Value="K" />
</asp:ListBox>
<asp:TextBox runat="server" ID="textBox" Text="8" />
<asp:Button runat="server" ID="button" Text="Select" OnClientClick="setSelectedIndex(); return false;" />
</div>
</form>
</body>
</html>