I actually accomplished this using the FileSystem Object along with a
recordset object to put the text file's contents into the table.  My sample
code is below:

Dim streamCurrent As TextStream
Dim fso As FileSystemObject
Dim objFolder As Folder
Dim objTextFilesIncoming As Files
Dim objTextFile As File
Dim rst As DAO.Recordset

Dim sPathText As String
sPathText = "C:\TEMP\VBAPDFTester\Export Text"
Set rst = CurrentDb.OpenRecordset("Table1")

' Loop through the Text files to insert the data into the Table
For Each objTextFile In objTextFilesIncoming
   ' Open the file as a stream object
   Set streamCurrent = objTextFile.OpenAsTextStream(ForReading,
TristateUseDefault)
   ' Insert the Data from the Text File.  Use a Recordset so that quotes
get inserted properly.
   rst.AddNew
   rst!FullText = streamCurrent.ReadAll
   rst.Update
   
   ' Close the Text Stream object so we can delete the file after we
inserted the text into the database
   streamCurrent.Close
   Set streamCurrent = Nothing
   
   'objTextFile.Copy sProcessedFileName
   'objTextFile.Delete True
Next