I have an ASP.Net page with a C# code behind.
However, I've been asked to not use a code behind - so that it will be easier to deploy in SharePoint.
Is there a way to include the C# code in the ASP.Net page, without using a separate code behind file?
By default Sharepoint does not allow server-side code to be executed in ASPX files. See this for how to resolve that.
However, I would raise that having a code-behind is not necessarily difficult to deploy in Sharepoint (we do it extensively) - just compile your code-behind classes into an assembly and deploy it using a solution.
If still no, you can include all the code you'd normally place in a codebehind like so:
<script language="c#" runat="server">
public void Page_Load(object sender, EventArgs e)
{
//hello, world!
}
</script>