The AI spending ages thinking through its turn isn't Total War: Rome II's only problem, but it is one you'll encounter awfully often. The second big patch hit today, with changes including reducing the AI's turn time, bug fixes, bags of balance tweaks, and more.
The 96-point patch notes say the AI turn time improvements have the "greatest effect during early game," but I'd be surprised if developer The Creative Assembly left it at that. You'll also find detailed plenty of crash fixes, performance improvements, smarter AI, and more.
The patch will download automatically through Steam.
Rome II's creative director apologised for the game's poor state at launch, and The Creative Assembly had planned to release weekly patches. That routine may not have lasted even until the second patch but look, do you want the game fixed or not?