CAD tip # 11732:

The re-sorted parts list can be then renumbered starting by 1.

On Error Resume Next
Dim oDwgDoc As DrawingDocument
oDwgDoc = ThisApplication.ActiveDocument

Dim oPartsList1 As PartsList
oPartsList1 = oDwgDoc.ActiveSheet.PartsLists.Item(1)
If oPartsList1 Is Nothing Then
	MsgBox ("No parts list!")
Else
	oPartsList1.Sort("PART NUMBER") ' Needs to be localized: e.g. BAUTEILNUMMER (de), ČÍSLO SOUČÁSTI (cz)
	oPartsList1.Renumber
End If 

If you need to change sort order of your assembly BOM in a similar way, use the following iLogic rule:

'Get active assembly
Dim activeAssembly As AssemblyDocument = ThisApplication.ActiveDocument
'Get structured bom view
Dim bomView As BOMView = activeAssembly.ComponentDefinition.BOM.BOMViews(2)
'Sort by Part Number
Call bomView.Sort("Part Number", True)
'Renumber rows
Call bomView.Renumber(1, 1)