A Microsoft ODBC driver for Paradox databases comes with Windows, so you can certainly connect to Paradox tables using ADO and ODBC. See the 32- and 64-bit ODBC administration apps under Control Panel | Administrative Tools, and in particular its Drivers tab.
To create a simple Paradox + ADO app:
Use Windows' ODBC wizard to create a system- or file-DSN that uses the MS ODBC Driver for ODBC to connect to the Paradox table.
In your Delphi app, use a TAdoConnection to use e.g. the OLE DB provider for ODBC to use the DSN and a TAdoQuery to do a SELECT * from the P'Dox table.
See my answer here
BDE to ADO conversion in DELPHI 5
for a way of converting from BDE to ADO to access Paradox tables. Btw, once you have access to your Paradox data via ADO, it is straightforward to replace Paradox with a proper, robust RDBMS.
Recent versions of Dephi, including Tokyo, come with a very capable alternative DB-access library called FireDAC, but:
It has a much steeper learning curve than ADO.
Its author no longer works for Embarcadero, so with their numerous other lay-offs, FireDAC may become an "evolutionary dead-end."
Being from Embarcadero, it does not have the "safety in numbers" that comes with using MS's tried and tested ADO.