Create a Macro that uses the TransferText command to import one of your text files (you will probably need to do it manually once to create an Import Specification to use).
Then, convert the Macro to Visual Basic code (using the Utility found on the Macro ribbon). They, you should be able to swap out your TransferSpreadsheet action with the TransferText action.
Also be sure to update your strFile variable so that it references the extension you are using for your text files, i.e.
Code:
strFile = Dir(strPath & "\*.txt")