Repurposing FT232 UART pins as parallel out
So, you want to light one digit at a time, which means you need to select 1 of 6 anodes to drive (3 bits) and 1 of 10 cathodes (4 bits), for a total of 7 bits of output.

The FT232R has modes that directly support this. Read the paragraphs "Asynchronous  Bit Bang Mode with RD# and WR# Strobes." and "Synchronous Bit Bang Mode." on page 14 of the datasheet. Synchronous is probably what you want. There's an application note that goes into additional detail.