@Josh_Waldner in its simplest form, it would be something like below :-
Application.CutCopyMode = False
Dim rngSumRange As Range
Set rngSumRange = Range(ActiveCell.Offset(-1, 0), ActiveCell.Offset(-1, 0).End(xlUp))
ActiveCell.Formula = "=SUM(" & rngSumRange.Address & ")"
Though it is not as intelligent as autosum button
Example, below column, autosum button sums as 123, but above simple macro sums as zero. I am not sure of what all behaviour and checks are there in autosum button, but if one can list, then perhaps with more sophisticated macro, one can emulate it in VBA.