Unfortunately, there are currently no ATMs inside the port. The nearest ATM is in Piazzale degli Eroi, 2; at 100 meters from Forte Michelangelo: to reach it, exit the port at Varco Fortezza and take Via Giuseppe Garibaldi.
Or you can find it near the train station of Civitavecchia, if you go to Rome by train. Or if you go to Rome with a private transfer service, you can ask your driver to make a stop at the nearest ATM