Probably the easiest thing to do is to link to the files one at a time. When you do it, name the resulting table something generic, tblIncomingData. Then create an append query that appends the tblIncomingData to another table with all the records in it.
The key is creating a Link Specification that you can use with the TransferText method of the DoCmd object. To start, choose File/Get External Data/Link. Then when the linking wizard comes up, hit the Advanced button. There you tell access whether it is a delimited file or a fixed file, the fieldnames and types. Make sure to save and name the specification, then you can use it with the TransferText method and write a few more lines of code to import all the files.