There are few steps required to bind Choice field column with dropdownlist.The code is under here:

Guid
siteId = SPContext.Current.Site.ID;
SPSecurity.RunWithElevatedPrivileges(delegate()
{

using (SPSite site = new SPSite(siteId))
{
using (SPWeb objSPWeb = site.RootWeb)
{
SPList objSPList = objSPWeb.Lists["ListName"];

SPFieldChoice field = (SPFieldChoice)objSPList.Fields["Column Name"];
DropDownList1.DataSource = field.Choices;
DropDownList1.DataBind();
}
}
});