Let say wrd is your instance of Word, aDoc your document and you want (for the first table in your document) to move the row with index src just before the row with index dest, you couyld write something like this (adding all the necessary checks):
Table tbl = aDoc.Tables[1];
Row toMove = tbl.Rows[src];
object beforeRow = tbl.Rows[dest];
Row newRow = tbl.Rows.Add(ref beforeRow);
toMove.Select();
wrd.Selection.Copy();
newRow.Select();
wrd.Selection.Paste();
toMove.Delete();
newRow.Delete();