In accordance with your description and with the connectors' ends centred on the cells, this code generates msoConnectorStraight forms on the RangeToConnect parameter.
Note: One line controls whether empty rows should be skipped; comment it if you choose.
Sub ConnectValues(RangeToConnect As Range)
Dim ws As Worksheet
Set ws = RangeToConnect.Parent
'Clear the existing shapes on the range
Dim s As Shape
For Each s In ws.Shapes
If s.Type = msoConnectorStraight And _
Not Application.Intersect(RangeToConnect, s.TopLeftCell) Is Nothing And _
Not Application.Intersect(RangeToConnect, s.BottomRightCell) Is Nothing Then
s.Delete
End If
Next s
'Add the connectors to the range
Dim cell1 As Range, cell2 As Range, r As Range, c As Range
For Each r In RangeToConnect.Rows
Set cell2 = cell1
Set cell1 = Nothing 'Breaks the line on empty rows, to be commented if they should be ignored.
For Each c In r.Cells
If VBA.Len(c.Value) > 0 Then
Set cell1 = c
Exit For
End If
Next c
If Not cell1 Is Nothing And Not cell2 Is Nothing Then
ws.Shapes.AddConnector _
msoConnectorStraight, _
cell1.Left + cell1.Width / 2, cell1.Top + cell1.Height / 2, _
cell2.Left + cell2.Width / 2, cell2.Top + cell2.Height / 2
End If
Next r
End Sub