I'm not sure you can.
But you could copy that column (visible cells only) to a new sheet (in column
A), autofit that column, keep track of the width and use it on the original
column.
Option Explicit
Sub testme()
Dim curWks As Worksheet
Dim tempWks As Worksheet
Dim rng As Range
Dim myWidth As Double
Set curWks = ActiveSheet '???
Set tempWks = Worksheets.Add
With curWks
Set rng = Nothing
On Error Resume Next
Set rng = .Range("a:a").Cells.SpecialCells(xlCellTypeVisible)
On Error GoTo 0
If rng Is Nothing Then
'no visible cells, what to do?
Else
rng.Copy _
Destination:=tempWks.Range("a1")
tempWks.Range("a1").EntireColumn.ColumnWidth = 255
tempWks.Range("a1").EntireColumn.AutoFit
myWidth = tempWks.Range("a1").ColumnWidth
.Range("a1").ColumnWidth = myWidth
End If
End With
Application.DisplayAlerts = False
tempWks.Delete
Application.DisplayAlerts = True
End Sub