As noted in another answer, the official word from Microsoft is to open an Access 97 file in Access 2003 and upgrade it to a newer file format. Unfortunately, from now on many people will have difficulty getting their hands on a legitimate copy of Access 2003 (or any other version prior to Access 2013, or whatever the latest version happens to be).
In that case, a possible workaround would be to
- install a 32-bit version of SQL Server Express Edition, and then
- have the SQL Server import utility use Jet* ODBC to import the tables into SQL Server.
I just tried that with a 32-bit version of SQL Server 2008 R2 Express Edition and it worked for me. Access 2013 adamantly refused to have anything to do with the Access 97 file, but SQL Server imported the tables without complaint.
At that point you could import the tables from SQL Server into an Access 2013 database. Or, if your goal was simply to get the data out of the Access 97 file then you could continue to work with it in SQL Server, or move it to some other platform, or whatever.
*Important: The import needs to be done using the older Jet ODBC driver ...
Microsoft Access Driver (*.mdb)
... which ships with Windows but is only available to 32-bit applications. The Access 2013 version of the newer Access Database Engine ("ACE") ODBC driver ...
Microsoft Access Driver (*.mdb, *.accdb)
also refuses to read Access 97 files (with the same error message cited in the question).