Try this:
rng.AutoFilter 1, "="
rng.SpecialCells(xlCellTypeVisible).EntireRow.Delete
ActiveSheet.AutoFilterMode = False '~~> removes the filter
This filter out blanks or zero length strings then deletes it.
Or you can directly filter A1:A10
like this:
Range("A1:A10").AutoFilter 1, 10
Range("A1:A10").SpecialCells(xlCellTypeVisible).EntireRow.Delete
ActiveSheet.AutoFilterMode = False