One way you can do this is to get the renderer for the currentcell, and then if it is a textbox, set the SelectionStart and Selection.Len. Here is a snippet that positions the cursor at the end of the text in CurrentCellStartEditing.
private void gridControl1_CurrentCellStartEditing(object sender, System.ComponentModel.CancelEventArgs e)
{
GridTextBoxCellRenderer tbr = this.gridControl1.CurrentCell.Renderer as GridTextBoxCellRenderer;
if(tbr != null)
{
tbr.TextBox.SelectionStart = tbr.TextBox.Text.Length;
tbr.TextBox.SelectionLength = 0;
}
}