I presume by table you mean a table in Access, thus I think the suggestion won't do what you want since Select queries don't update. I say that because get the drift that your select query is for exporting to Excel, but you want the date it was run to be stored in Access.
You have not provided any clue about this process or details about where you want this date to go. You should be able to either call an update an append query, or run a sql statement in code. Which query you need depends on your target table. If there is no applicable record, there is nothing to update, thus the Append query is what you'd need. If there is, is it the only record? If not, you need a WHERE clause to tell Access which record to update. The value you'd update or append to the table would be Date() if you want only the date, or Now() if you want the time as well. The sql statement for a single record date table might look something like
UPDATE tblExportDate SET tblExportDate.DateRan = Date
You will have to provide more info on the process and table(s) if I'm on the right track and you need more help.
Note: in case you are not aware, Date is a reserved word and should never be used for a field, table or object name.