It looks like you just hard-coded the row and column; otherwise, a couple of small tweaks, and I think you're there:
Dim sh As Worksheet
Dim rw As Range
Dim RowCount As Integer
RowCount = 0
Set sh = ActiveSheet
For Each rw In sh.Rows
If sh.Cells(rw.Row, 1).Value = "" Then
Exit For
End If
RowCount = RowCount + 1
Next rw
MsgBox (RowCount)